<?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>0001630117</rptOwnerCik>
            <rptOwnerName>Schomburger Jeffrey K</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>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-02-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2700</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>74.83</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7023.15</value>
                    <footnoteId id="F2"/>
                </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>
        <footnote id="F2">Includes 2,029.221 shares of the Issuer's Class A Common Stock acquired by the Reporting Person pursuant to the Deferred Fee Plan for Directors, which 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 Jeffrey Schomburger</signatureName>
        <signatureDate>2018-02-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-02-08
0
0000100493
TYSON FOODS INC
TSN
0001630117
Schomburger Jeffrey K
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
Class A Common Stock
2018-02-09
4
P
0
2700
74.83
A
7023.15
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 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.
Includes 2,029.221 shares of the Issuer's Class A Common Stock acquired by the Reporting Person pursuant to the Deferred Fee Plan for Directors, which 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 Jeffrey Schomburger
2018-02-12