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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-05-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001703544</rptOwnerCik>
            <rptOwnerName>Ramsey Douglas Wayne</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President Poultry</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4992.4788</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>95.3337</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Employee Stock Purchase Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-05-12</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10645.604</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15638.0828</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Includes 2,172.3438 shares of Class A Common Stock which vest on November 21, 2017; 1,525.309 shares of Class A Common Stock which vest on November 30, 2018 and 1,294.826 shares of Class A Common Stock which vest on November 28, 2019.</footnote>
        <footnote id="F2">Award of Class A Common Stock which vests on May 12, 2020 if the performance metric described in the applicable Stock Incentive Agreement (the Incentive Agreement) is achieved and the Reporting Person is employed by the Issuer on the vesting date. The performance metrics are achievement of a two year (fiscal 2017-2019) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metric is not achieved, the award expires.</footnote>
        <footnote id="F3">Includes 2,172.3438 shares of Class A Common Stock which vest on November 21, 2017; 1,525.309 shares of Class A Common Stock which vest on November 30, 2018; 1,294.826 shares of Class A Common Stock which vest on November 28, 2019 and 10,645.604 shares of Class A Common Stock which vest on May 12, 2020.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Douglas W. Ramsey</signatureName>
        <signatureDate>2017-05-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-05-12
0
0000100493
TYSON FOODS INC
TSN
0001703544
Ramsey Douglas Wayne
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
President Poultry
Class A Common Stock
4992.4788
D
Class A Common Stock
95.3337
I
Employee Stock Purchase Plan
Class A Common Stock
2017-05-12
4
A
0
10645.604
0
A
15638.0828
D
Includes 2,172.3438 shares of Class A Common Stock which vest on November 21, 2017; 1,525.309 shares of Class A Common Stock which vest on November 30, 2018 and 1,294.826 shares of Class A Common Stock which vest on November 28, 2019.
Award of Class A Common Stock which vests on May 12, 2020 if the performance metric described in the applicable Stock Incentive Agreement (the Incentive Agreement) is achieved and the Reporting Person is employed by the Issuer on the vesting date. The performance metrics are achievement of a two year (fiscal 2017-2019) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metric is not achieved, the award expires.
Includes 2,172.3438 shares of Class A Common Stock which vest on November 21, 2017; 1,525.309 shares of Class A Common Stock which vest on November 30, 2018; 1,294.826 shares of Class A Common Stock which vest on November 28, 2019 and 10,645.604 shares of Class A Common Stock which vest on May 12, 2020.
/s/ Douglas W. Ramsey
2017-05-17