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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-12-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001200996</rptOwnerCik>
            <rptOwnerName>MCNAMARA KEVIN M</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>2015-12-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>608.741</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>58988.741</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>2016-02-05</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2626.97</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>57.10</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>61615.711</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of the Issuer's Class A Common Stock received by the Reporting Person pursuant to a dividend reinvestment feature under Issuer's stock plan since the last Statement of Changes in Beneficial Ownership was filed by the Reporting Person. Such acquisitions are exempt from Section 16 reporting requirements pursuant to Rule 16a-11.</footnote>
        <footnote id="F2">Includes 44,844.693 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>
        <footnote id="F3">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 held on February 5, 2016. 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 by power of Attorney for Kevin M. McNamara</signatureName>
        <signatureDate>2016-02-09</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2015-12-17
0
0000100493
TYSON FOODS INC
TSN
0001200996
MCNAMARA KEVIN M
2200 DON TYSON PARKWAY
SPRINGDALE
AR
72762
1
0
0
0
Class A Common Stock
2015-12-17
4
J
0
608.741
0
A
58988.741
D
Class A Common Stock
2016-02-05
4
J
0
2626.97
57.10
A
61615.711
D
Represents shares of the Issuer's Class A Common Stock received by the Reporting Person pursuant to a dividend reinvestment feature under Issuer's stock plan since the last Statement of Changes in Beneficial Ownership was filed by the Reporting Person. Such acquisitions are exempt from Section 16 reporting requirements pursuant to Rule 16a-11.
Includes 44,844.693 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.
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 held on February 5, 2016. 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 by power of Attorney for Kevin M. McNamara
2016-02-09