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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-11-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001673248</rptOwnerCik>
            <rptOwnerName>McGurk Monica H</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 WEST 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>EVP, Strategy &amp; New Ventures</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-11-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>9393.512</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9393.512</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>58.34</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-11-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>40836</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>58.34</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2017-11-28</value>
            </exerciseDate>
            <expirationDate>
                <value>2026-11-28</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>40836.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>40836</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-11-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>18787.024</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>18787.024</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18787.024</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Award of Class A Common Stock which vests on November 18, 2019 if the performance metric described in the applicable Stock Incentive Agreement are achieved. The performance metric is achievement of a three year (fiscal 2017-2019) cumulative EBIT target as set forth in the Stock Incentive Agreement. If the performance metric is not achieved, the award expires.</footnote>
        <footnote id="F2">Represents 9,393.512 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable Stock Incentive Agreement is achieved.</footnote>
        <footnote id="F3">The stock options vest at 33 1/3% on each of the first, second, and third anniversary dates of the grant.</footnote>
        <footnote id="F4">Award of performance Class A Common Stock which vests on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved. The performance metric set forth in the Stock Incentive Agreement are (1) achievement of a three year (fiscal 2017-2019) cumulative EBIT target and (2) a favorable comparison of the relative total shareholder return of the Issuer's Class A Common Stock compared to a predetermined peer group of publicly traded companies over a three year (fiscal 2017-2019) period. Subject to the achievement of the performance metric, the performance shares could vest at a level of 50%-200% and are reported as derivative securities at the 200% level. If neither of the performance metrics are achieved, the award expires.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Monica H. McGurk</signatureName>
        <signatureDate>2016-11-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2016-11-28
0
0000100493
TYSON FOODS INC
TSN
0001673248
McGurk Monica H
2200 WEST DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
EVP, Strategy & New Ventures
Class A Common Stock
2016-11-28
4
A
0
9393.512
0
A
9393.512
D
Non-Qualified Stock Options (Right to Buy)
58.34
2016-11-28
4
A
0
40836
58.34
A
2017-11-28
2026-11-28
Class A Common Stock
40836.0
40836
D
Performance Shares
2016-11-28
4
A
0
18787.024
A
Class A Common Stock
18787.024
18787.024
D
Award of Class A Common Stock which vests on November 18, 2019 if the performance metric described in the applicable Stock Incentive Agreement are achieved. The performance metric is achievement of a three year (fiscal 2017-2019) cumulative EBIT target as set forth in the Stock Incentive Agreement. If the performance metric is not achieved, the award expires.
Represents 9,393.512 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable Stock Incentive Agreement is achieved.
The stock options vest at 33 1/3% on each of the first, second, and third anniversary dates of the grant.
Award of performance Class A Common Stock which vests on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved. The performance metric set forth in the Stock Incentive Agreement are (1) achievement of a three year (fiscal 2017-2019) cumulative EBIT target and (2) a favorable comparison of the relative total shareholder return of the Issuer's Class A Common Stock compared to a predetermined peer group of publicly traded companies over a three year (fiscal 2017-2019) period. Subject to the achievement of the performance metric, the performance shares could vest at a level of 50%-200% and are reported as derivative securities at the 200% level. If neither of the performance metrics are achieved, the award expires.
/s/ Monica H. McGurk
2016-11-30