<?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>0001207117</rptOwnerCik>
            <rptOwnerName>MILLER CHERYL</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>4323.15</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 Issuer's Director Compensation Policy, the Reporting Person elected to take this stock award in lieu of a deferred stock award otherwise granted to the Issuer's non-employee directors.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson as Power of Attorney for Cheryl S. Miller</signatureName>
        <signatureDate>2018-02-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-02-08
0
0000100493
TYSON FOODS INC
TSN
0001207117
MILLER CHERYL
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
4323.15
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 Issuer's Director Compensation Policy, the Reporting Person elected to take this stock award in lieu of a deferred stock award otherwise granted to the Issuer's non-employee directors.
/s/ R. Read Hudson as Power of Attorney for Cheryl S. Miller
2018-02-12