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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-02-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001722101</rptOwnerCik>
            <rptOwnerName>Banks Samuel Dean Jr</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>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>2018-02-08</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2029.221</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>73.92</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2029.221</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 Annual Meeting of Shareholders held on February 8, 2018.  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 Samuel Dean Banks, Jr.</signatureName>
        <signatureDate>2018-02-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-02-08
0
0000100493
TYSON FOODS INC
TSN
0001722101
Banks Samuel Dean Jr
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
1
0
0
0
Class A Common Stock
2018-02-08
4
A
0
2029.221
73.92
A
2029.221
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 Annual Meeting of Shareholders held on February 8, 2018.  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 Samuel Dean Banks, Jr.
2018-02-12