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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-02-05</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001649956</rptOwnerCik>
            <rptOwnerName>Durham Mikel A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 DON TYSON PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SPRINGDALE</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72762</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-02-05</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2626.97</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>57.10</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2626.97</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents a stock award for shares of the Issuer's Class A Common Stock having a value of $150,000 granted on the date of election as a director at the 2016 Annual Meeting of Shareholders (February 5, 2016).  Per the Deferred Fee Plan for Directors, these shares shall vest 180 days after termination of the Reporting Person's service as a member of the Issuer's board of directors.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson as Power of Attorney for Mikel A. Durham</signatureName>
        <signatureDate>2016-02-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2016-02-05
0
0000100493
TYSON FOODS INC
TSN
0001649956
Durham Mikel A.
2200 DON TYSON PARKWAY
SPRINGDALE
AR
72762
1
0
0
0
Class A Common Stock
2016-02-05
4
J
0
2626.97
57.10
A
2626.97
D
Represents a stock award for shares of the Issuer's Class A Common Stock having a value of $150,000 granted on the date of election as a director at the 2016 Annual Meeting of Shareholders (February 5, 2016).  Per the Deferred Fee Plan for Directors, these shares shall vest 180 days after termination of the Reporting Person's service as a member of the Issuer's board of directors.
/s/ R. Read Hudson as Power of Attorney for Mikel A. Durham
2016-02-09