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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-11-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001552992</rptOwnerCik>
            <rptOwnerName>Hayes Thomas P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>400 S. JEFFERSON STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60607</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President, Food Service</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>7690</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7690</value>
                </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>42.26</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>83490</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.26</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2015-11-21</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-11-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>83490.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>83490</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>24609</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>24609.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>24609</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 the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2017 fiscal year if the performance metrics described in the applicable Stock Incentive Agreement (the Incentive Agreement) are achieved. The performance metrics are achievement of a three year (fiscal 2015-2017) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metrics are not achieved, the award expires.</footnote>
        <footnote id="F2">Award of performance Class A Common Stock which vests on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2017 fiscal year if the performance metrics described in the applicable Stock Incentive Agreement (the Incentive Agreement) are achieved. The performance metrics are (1) achievement of a three year (fiscal 2015-2017) cumulative EBIT target as set forth in the Incentive Agreement and (2) a comparison of the market price of the Issuer's Class A Common Stock to a peer group of publicly traded companies selected by the Compensation Committee of the Board of Directors of Issuer over a three year (fiscal 2015-2017) period, as more particularly described in the Incentive Agreement. If neither of the performance metrics is achieved, the award expires.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by Power of Attorney for Thomas P. Hayes</signatureName>
        <signatureDate>2014-11-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2014-11-21
0
0000100493
TYSON FOODS INC
TSN
0001552992
Hayes Thomas P
400 S. JEFFERSON STREET
CHICAGO
IL
60607
0
1
0
0
President, Food Service
Class A Common Stock
2014-11-21
4
A
0
7690
0
A
7690
D
Non-Qualified Stock Options (Right to Buy)
42.26
2014-11-21
4
A
0
83490
42.26
A
2015-11-21
2024-11-21
Class A Common Stock
83490.0
83490
D
Performance Shares
2014-11-21
4
A
0
24609
A
Class A Common Stock
24609.0
24609
D
Award of Class A Common Stock which vests on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2017 fiscal year if the performance metrics described in the applicable Stock Incentive Agreement (the Incentive Agreement) are achieved. The performance metrics are achievement of a three year (fiscal 2015-2017) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metrics are not achieved, the award expires.
Award of performance Class A Common Stock which vests on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2017 fiscal year if the performance metrics described in the applicable Stock Incentive Agreement (the Incentive Agreement) are achieved. The performance metrics are (1) achievement of a three year (fiscal 2015-2017) cumulative EBIT target as set forth in the Incentive Agreement and (2) a comparison of the market price of the Issuer's Class A Common Stock to a peer group of publicly traded companies selected by the Compensation Committee of the Board of Directors of Issuer over a three year (fiscal 2015-2017) period, as more particularly described in the Incentive Agreement. If neither of the performance metrics is achieved, the award expires.
/s/ R. Read Hudson by Power of Attorney for Thomas P. Hayes
2014-11-25