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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-11-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001554533</rptOwnerCik>
            <rptOwnerName>Grimes Sally</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>Pres and Global Growth Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-11-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>52</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>52</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>2014-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>7690</value>
                    <footnoteId id="F2"/>
                </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="F3"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>24609</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </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">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 reporting requirements pursuant to Rule 16b-3.</footnote>
        <footnote id="F2">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="F3">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 Sally Grimes</signatureName>
        <signatureDate>2014-11-25</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2014-11-20
0
0000100493
TYSON FOODS INC
TSN
0001554533
Grimes Sally
400 S. JEFFERSON STREET
CHICAGO
IL
60607
0
1
0
0
Pres and Global Growth Officer
Class A Common Stock
2014-11-20
4
J
0
52
0
A
52
I
Employee Stock Purchase Plan
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
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 reporting requirements pursuant to Rule 16b-3.
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 Sally Grimes
2014-11-25