content: <PAGE>   1
       AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JUNE 29, 1998
                                                     REGISTRATION NO. 333-________
  ================================================================================
  
                        SECURITIES AND EXCHANGE COMMISSION
                               Washington, D.C. 20549
  
                        -----------------------------------
  
                                      FORM S-8
  
              REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
  
                        -----------------------------------
  
                             DELL COMPUTER CORPORATION
               (Exact name of registrant as specified in its charter)
  
             DELAWARE                                    74-2487834
   (State or other jurisdiction of          (I.R.S. Employer Identification No.)
    incorporation or organization)
  
    ONE DELL WAY, ROUND ROCK, TEXAS                      78682-2244
  (Address of principal executive offices)               (Zip code)
  
  
                      DELL COMPUTER CORPORATION INCENTIVE PLAN
                              (Full title of the plan)
  
               THOMAS B. GREEN                                Copies to:
  SENIOR VICE PRESIDENT, LAW AND ADMINISTRATION           THOMAS H. WELCH, JR.
          DELL COMPUTER CORPORATION                   GENERAL CORPORATE COUNSEL
                 ONE DELL WAY                         DELL COMPUTER CORPORATION
         ROUND ROCK, TEXAS 78682-2244                        ONE DELL WAY
    (Name and address of agent for service)         ROUND ROCK, TEXAS 78682-2244
  
                                   (512) 338-4400
           (Telephone number, including area code, of agent for service)
           -------------------------------------------------------------
  
                          CALCULATION OF REGISTRATION FEE
  <TABLE>
  <CAPTION>
  ===========================================================================================================
                                                   PROPOSED               PROPOSED
  TITLE OF SECURITIES      AMOUNT TO BE        MAXIMUM OFFERING       MAXIMUM AGGREGATE         AMOUNT OF
  TO BE REGISTERED          REGISTERED        PRICE PER SHARE(1)       OFFERING PRICE       REGISTRATION FEE
  <S>                    <C>                  <C>                     <C>                   <C>
  Common Stock           35,654,140 shares         $86.8049            $3,094,954,057            $913,011
  ===========================================================================================================
  </TABLE>
  
  (1)  Estimated solely for the purpose of calculating the registration fee in
       accordance with Rule 457(h) promulgated under the Securities Act of 1933,
       based on the average of the high and low prices for Registrant's common
       stock reported in The Nasdaq Stock Market on June 22, 1998.
  
  (2)  Pursuant to Rule 416, this Registration Statement shall be deemed to cover
       such additional shares of the Registrant's common stock as may become
       issuable pursuant to the antidilution provisions of the Dell Computer
       Corporation Incentive Plan.
  <PAGE>   2
  Pursuant to General Instruction E of Form S-8 ("Registration of Additional
  Securities"), the Registrant hereby makes the following statement:
  
           On July 14, 1994, the Registrant filed with the Securities and
           Exchange Commission a Registration Statement on Form S-8 (Registration
           No. 33-54577) (the "Prior Registration Statement") relating to shares
           of the Registrant's common stock to be issued pursuant to the Dell
           Computer Corporation Incentive Plan (the "Incentive Plan"), and the
           Prior Registration Statement is currently effective.  This
           Registration Statement relates to securities (a) of the same class as
           those to which the Prior Registration Statement relates and (b) to be
           issued pursuant to the Incentive Plan.  The contents of the Prior
           Registration Statement are incorporated herein by reference.
  
  The following exhibits are filed as a part of this Registration Statement:
  
     EXHIBIT NO.                      DESCRIPTION OF EXHIBIT        
  ----------------      -------------------------------------------------------
  
         5              Opinion of Thomas H. Welch, Jr., General Corporate Counsel
  
        23.1            Consent of Price Waterhouse LLP
  
        23.2            Consent of Legal Counsel (included in Exhibit 5)
  
        24              Power of Attorney (set forth on Page 3)            
  
  
  
  
  
  
  
  
                                         2
  <PAGE>   3
                                     SIGNATURES
  
       Pursuant to the requirements of the Securities Act of 1933, the Registrant
  certifies that it has reasonable grounds to believe that it meets all of the
  requirements for filing on Form S-8 and has duly caused this Registration
  Statement to be signed on its behalf by the undersigned, thereunto duly
  authorized, in the City of Round Rock, Texas on June 29, 1998.
  
                                          DELL COMPUTER CORPORATION
  
                                          By: /s/ MICHAEL S. DELL
                                             ------------------------------------
                                             Michael S. Dell,
                                             Chairman and Chief Executive Officer
  
  
       Pursuant to the requirements of the Securities Act of 1933, this
  Registration Statement has been signed by the following persons in the
  capacities and on the dates indicated.  Each person whose signature appears
  below hereby authorizes and appoints each of Michael S. Dell and Thomas B.
  Green as his or her attorney-in-fact to sign on his or her behalf individually
  and in the capacity stated below all amendments and post-effective amendments
  to this registration statement as that attorney-in-fact may deem necessary or
  appropriate.
  
  <TABLE>
  <CAPTION>
          SIGNATURE                          CAPACITY                       DATE
          ---------                          --------                       ----
  <S>                              <C>                                   <C>
  
  /s/ MICHAEL S. DELL              Chairman of the Board and             June 29, 1998
  ---------------------------         Chief Executive Officer                         
      Michael S. Dell                 (principal executive officer)                   
                                                                                      
                                                                                      
  /s/ DONALD J. CARTY              Director                              June 29, 1998
  ---------------------------                                                          
      Donald J. Carty                                                                 
                                                                                      
                                                                                      
  /s/ PAUL O. HIRSCHBIEL, JR.       Director                              June 29, 1998
  ---------------------------                                                          
      Paul O. Hirschbiel, Jr.                                                          
                                                                                      
                                                                                      
  /s/ MICHAEL H. JORDAN            Director                              June 29, 1998
  ---------------------------                                                          
      Michael H. Jordan                                                               
                                                                                      
                                                                                      
  /s/ THOMAS W. LUCE III           Director                              June 29, 1998
  ---------------------------                                                          
      Thomas W. Luce III                                                              
                                                                                      
                                                                                      
  /s/ KLAUS S. LUFT                Director                              June 29, 1998
  ---------------------------                                                          
      Klaus S. Luft
  </TABLE>
  
                                         3
  <PAGE>   4
  
  <TABLE>
  <CAPTION>
          SIGNATURE                          CAPACITY                       DATE
          ---------                          --------                       ----
  <S>                              <C>                                   <C>
  
  /s/ CLAUDINE B. MALONE
  --------------------------       Director                              June 29, 1998
      Claudine B. Malone           
  
  
  /s/ ALEX J. MANDL
  --------------------------       Director                              June 29, 1998
      Alex J. Mandl
  
  
  /s/ MICHAEL A. MILES 
  --------------------------       Director                              June 29, 1998
      Michael A. Miles 
  
  
  /s/ THOMAS J. MEREDITH 
  --------------------------       Senior Vice President and             June 29, 1998
      Thomas J. Meredith             Chief Financial Officer
                                     (principal financial officer)
  
  /s/ JAMES M. SCHNEIDER
  --------------------------       Vice President - Finance and          June 29, 1998
      James M. Schneider             Chief Accounting Officer
                                     (principal accounting officer)
  </TABLE>
  
  
  
                                         4
  <PAGE>   5
                                   EXHIBIT INDEX
  
  
  <TABLE>
  <CAPTION>
  EXHIBIT NO.                           DESCRIPTION OF EXHIBIT
  -----------      ---------------------------------------------------------------
    <S>            <C>
     5             Opinion of Thomas H. Welch, Jr., General Corporate Counsel
    23.1           Consent of Price Waterhouse LLP
    23.2           Consent of Legal Counsel (included in Exhibit 5)
    24             Power of Attorney (set forth on Page 3)
  </TABLE>
metadata_documents: [{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 10227}]
metadata_filer: {"company-data": {"conformed-name": "DELL COMPUTER CORP", "cik": "0000826083", "assigned-sic": "3571", "irs-number": "742487834", "state-of-incorporation": "DE", "fiscal-year-end": "0131"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-58039", "film-number": "98657183"}, "business-address": {"street1": "ONE DELL WAY", "city": "ROUND ROCK", "state": "TX", "zip": "78682-2244", "phone": "5123384400"}, "mail-address": {"street1": "ONE DELL WAY", "city": "ROUND ROCK", "state": "TX", "zip": "78682"}}
text: 1
       AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JUNE 29, 1998
                                                     REGISTRATION NO. 333-________
  ================================================================================
  
                        SECURITIES AND EXCHANGE COMMISSION
                               Washington, D.C. 20549
  
                        -----------------------------------
  
                                      FORM S-8
  
              REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
  
                        -----------------------------------
  
                             DELL COMPUTER CORPORATION
               (Exact name of registrant as specified in its charter)
  
             DELAWARE                                    74-2487834
   (State or other jurisdiction of          (I.R.S. Employer Identification No.)
    incorporation or organization)
  
    ONE DELL WAY, ROUND ROCK, TEXAS                      78682-2244
  (Address of principal executive offices)               (Zip code)
  
                      DELL COMPUTER CORPORATION INCENTIVE PLAN
                              (Full title of the plan)
  
               THOMAS B. GREEN                                Copies to:
  SENIOR VICE PRESIDENT, LAW AND ADMINISTRATION           THOMAS H. WELCH, JR.
          DELL COMPUTER CORPORATION                   GENERAL CORPORATE COUNSEL
                 ONE DELL WAY                         DELL COMPUTER CORPORATION
         ROUND ROCK, TEXAS 78682-2244                        ONE DELL WAY
    (Name and address of agent for service)         ROUND ROCK, TEXAS 78682-2244
  
                                   (512) 338-4400
           (Telephone number, including area code, of agent for service)
           -------------------------------------------------------------
  
                          CALCULATION OF REGISTRATION FEE
  ===========================================================================================================
                                                   PROPOSED               PROPOSED
  TITLE OF SECURITIES      AMOUNT TO BE        MAXIMUM OFFERING       MAXIMUM AGGREGATE         AMOUNT OF
  TO BE REGISTERED          REGISTERED        PRICE PER SHARE(1)       OFFERING PRICE       REGISTRATION FEE
  Common Stock           35,654,140 shares         $86.8049            $3,094,954,057            $913,011
  ===========================================================================================================
  (1)  Estimated solely for the purpose of calculating the registration fee in
       accordance with Rule 457(h) promulgated under the Securities Act of 1933,
       based on the average of the high and low prices for Registrant's common
       stock reported in The Nasdaq Stock Market on June 22, 1998.
  
  (2)  Pursuant to Rule 416, this Registration Statement shall be deemed to cover
       such additional shares of the Registrant's common stock as may become
       issuable pursuant to the antidilution provisions of the Dell Computer
       Corporation Incentive Plan.
  2
  Pursuant to General Instruction E of Form S-8 ("Registration of Additional
  Securities"), the Registrant hereby makes the following statement:
  
           On July 14, 1994, the Registrant filed with the Securities and
           Exchange Commission a Registration Statement on Form S-8 (Registration
           No. 33-54577) (the "Prior Registration Statement") relating to shares
           of the Registrant's common stock to be issued pursuant to the Dell
           Computer Corporation Incentive Plan (the "Incentive Plan"), and the
           Prior Registration Statement is currently effective.  This
           Registration Statement relates to securities (a) of the same class as
           those to which the Prior Registration Statement relates and (b) to be
           issued pursuant to the Incentive Plan.  The contents of the Prior
           Registration Statement are incorporated herein by reference.
  
  The following exhibits are filed as a part of this Registration Statement:
  
     EXHIBIT NO.                      DESCRIPTION OF EXHIBIT        
  ----------------      -------------------------------------------------------
  
         5              Opinion of Thomas H. Welch, Jr., General Corporate Counsel
  
        23.1            Consent of Price Waterhouse LLP
  
        23.2            Consent of Legal Counsel (included in Exhibit 5)
  
        24              Power of Attorney (set forth on Page 3)            
  
                                         2
  3
                                     SIGNATURES
  
       Pursuant to the requirements of the Securities Act of 1933, the Registrant
  certifies that it has reasonable grounds to believe that it meets all of the
  requirements for filing on Form S-8 and has duly caused this Registration
  Statement to be signed on its behalf by the undersigned, thereunto duly
  authorized, in the City of Round Rock, Texas on June 29, 1998.
  
                                          DELL COMPUTER CORPORATION
  
                                          By: /s/ MICHAEL S. DELL
                                             ------------------------------------
                                             Michael S. Dell,
                                             Chairman and Chief Executive Officer
  
       Pursuant to the requirements of the Securities Act of 1933, this
  Registration Statement has been signed by the following persons in the
  capacities and on the dates indicated.  Each person whose signature appears
  below hereby authorizes and appoints each of Michael S. Dell and Thomas B.
  Green as his or her attorney-in-fact to sign on his or her behalf individually
  and in the capacity stated below all amendments and post-effective amendments
  to this registration statement as that attorney-in-fact may deem necessary or
  appropriate.
  SIGNATURE                          CAPACITY                       DATE
          ---------                          --------                       ----
  /s/ MICHAEL S. DELL              Chairman of the Board and             June 29, 1998
  ---------------------------         Chief Executive Officer                         
      Michael S. Dell                 (principal executive officer)                   
                                                                                      
                                                                                      
  /s/ DONALD J. CARTY              Director                              June 29, 1998
  ---------------------------                                                          
      Donald J. Carty                                                                 
                                                                                      
                                                                                      
  /s/ PAUL O. HIRSCHBIEL, JR.       Director                              June 29, 1998
  ---------------------------                                                          
      Paul O. Hirschbiel, Jr.                                                          
                                                                                      
                                                                                      
  /s/ MICHAEL H. JORDAN            Director                              June 29, 1998
  ---------------------------                                                          
      Michael H. Jordan                                                               
                                                                                      
                                                                                      
  /s/ THOMAS W. LUCE III           Director                              June 29, 1998
  ---------------------------                                                          
      Thomas W. Luce III                                                              
                                                                                      
                                                                                      
  /s/ KLAUS S. LUFT                Director                              June 29, 1998
  ---------------------------                                                          
      Klaus S. Luft
  3
  4
  SIGNATURE                          CAPACITY                       DATE
          ---------                          --------                       ----
  /s/ CLAUDINE B. MALONE
  --------------------------       Director                              June 29, 1998
      Claudine B. Malone           
  
  /s/ ALEX J. MANDL
  --------------------------       Director                              June 29, 1998
      Alex J. Mandl
  
  /s/ MICHAEL A. MILES 
  --------------------------       Director                              June 29, 1998
      Michael A. Miles 
  
  /s/ THOMAS J. MEREDITH 
  --------------------------       Senior Vice President and             June 29, 1998
      Thomas J. Meredith             Chief Financial Officer
                                     (principal financial officer)
  
  /s/ JAMES M. SCHNEIDER
  --------------------------       Vice President - Finance and          June 29, 1998
      James M. Schneider             Chief Accounting Officer
                                     (principal accounting officer)
  4
  5
                                   EXHIBIT INDEX
  EXHIBIT NO.                           DESCRIPTION OF EXHIBIT
  -----------      ---------------------------------------------------------------
  5             Opinion of Thomas H. Welch, Jr., General Corporate Counsel
    23.1           Consent of Price Waterhouse LLP
    23.2           Consent of Legal Counsel (included in Exhibit 5)
    24             Power of Attorney (set forth on Page 3)