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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-06-19</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>2018-06-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>708.882</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>117291.1397</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-06-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>890.5766</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13571.8113</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>2018-07-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9012</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>68.85</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>108279.1397</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of the Issuer's Class A Common Stock received by the Reporting Person pursuant to the Issuer's dividend reinvestment 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 16a-11.</footnote>
        <footnote id="F2">Includes 24,194.2832 shares of Class A Common Stock which vested as described in footnote 4; 12,985.7 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement (&quot;SIA&quot;) are achieved; 11,228.283 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; 2,629.984 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved; and 8,761.033 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="F3">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="F4">On July 1, 2018, 24,194.2832 shares of restricted Class A Common Stock vested. These shares were previously reported as beneficially owned by the Reporting Person. Pursuant to an election made by the Reporting Person, 9,012 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations.</footnote>
        <footnote id="F5">Includes 12,985.7 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement (&quot;SIA&quot;) are achieved; 11,228.283 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; 2,629.984 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved; and 8,761.033 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable SIA are achieved.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Brett Worlow by Power of Attorney for Noel White</signatureName>
        <signatureDate>2018-07-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_153081328279289.xml", "description": "FORM 4", "secsgml_size_bytes": 8708}]
X0306
4
2018-06-19
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
2018-06-19
4
J
0
708.882
0
A
117291.1397
D
Class A Common Stock
2018-06-28
4
J
0
890.5766
0
A
13571.8113
I
Employee Stock Purchase Plan
Class A Common Stock
2018-07-01
4
S
0
9012
68.85
D
108279.1397
D
Represents shares of the Issuer's Class A Common Stock received by the Reporting Person pursuant to the Issuer's dividend reinvestment 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 16a-11.
Includes 24,194.2832 shares of Class A Common Stock which vested as described in footnote 4; 12,985.7 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement ("SIA") are achieved; 11,228.283 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; 2,629.984 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved; and 8,761.033 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable SIA are achieved.
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.
On July 1, 2018, 24,194.2832 shares of restricted Class A Common Stock vested. These shares were previously reported as beneficially owned by the Reporting Person. Pursuant to an election made by the Reporting Person, 9,012 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations.
Includes 12,985.7 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement ("SIA") are achieved; 11,228.283 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; 2,629.984 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved; and 8,761.033 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable SIA are achieved.
/s/ Brett Worlow by Power of Attorney for Noel White
2018-07-05