<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-12-15</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000100493</issuerCik>
        <issuerName>TYSON FOODS INC</issuerName>
        <issuerTradingSymbol>TSN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001340962</rptOwnerCik>
            <rptOwnerName>White Noel W</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 W DON TYSON PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SPRINGDALE</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72762</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Grp Pres FM &amp; Intl</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-12-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>96.3275</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>12681.2347</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Employee Stock Purchase Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-12-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>24575</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>116582.2577</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-12-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>24575</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>24575</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Holding by White Family Foundation</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-12-22</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>24575</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>80.958</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Holding by White Family Foundation</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of the Issuer's Class A Common Stock purchased for the Reporting Person's account under the Issuer's Employee Stock Purchase Plan since the last Statement of Changes in Beneficial Ownership was filed by the Reporting Person.  Such acquisitions are exempt from Section 16 concurrent reporting requirements pursuant to Rule 16b-3.</footnote>
        <footnote id="F2">The Reporting Person transferred shares from his personal stock account into an account held by the White Family Foundation thereby changing the ownership of the Class A Common Stock from direct to indirect.</footnote>
        <footnote id="F3">Includes 23,907.4752 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement (SIA) are achieved and the Reporting Person is employed by Issuer on the vesting date; 12,831.763 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; 11,095.179 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; 2,598.808 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved; and 8,657.176 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable SIA are achieved.</footnote>
        <footnote id="F4">This is a weighted average price.  These shares were sold in multiple transactions on December 22, 2017 at prices ranging from $80.90 to $81.01, inclusive.  The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within this range.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by Power of Attorney for Noel W. White</signatureName>
        <signatureDate>2017-12-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-12-15
0
0000100493
TYSON FOODS INC
TSN
0001340962
White Noel W
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
Grp Pres FM & Intl
Class A Common Stock
2017-12-15
4
J
0
96.3275
0
A
12681.2347
I
Employee Stock Purchase Plan
Class A Common Stock
2017-12-20
4
J
0
24575
0
D
116582.2577
D
Class A Common Stock
2017-12-20
4
J
0
24575
0
A
24575
I
Holding by White Family Foundation
Class A Common Stock
2017-12-22
4
S
0
24575
80.958
D
0
I
Holding by White Family Foundation
Represents shares of the Issuer's Class A Common Stock purchased for the Reporting Person's account under the Issuer's Employee Stock Purchase Plan since the last Statement of Changes in Beneficial Ownership was filed by the Reporting Person.  Such acquisitions are exempt from Section 16 concurrent reporting requirements pursuant to Rule 16b-3.
The Reporting Person transferred shares from his personal stock account into an account held by the White Family Foundation thereby changing the ownership of the Class A Common Stock from direct to indirect.
Includes 23,907.4752 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement (SIA) are achieved and the Reporting Person is employed by Issuer on the vesting date; 12,831.763 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; 11,095.179 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; 2,598.808 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved; and 8,657.176 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable SIA are achieved.
This is a weighted average price.  These shares were sold in multiple transactions on December 22, 2017 at prices ranging from $80.90 to $81.01, inclusive.  The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within this range.
/s/ R. Read Hudson by Power of Attorney for Noel W. White
2017-12-26