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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-12-11</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001340962</rptOwnerCik>
            <rptOwnerName>White Noel W</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President Poultry</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-12-11</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>12500</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>52.48</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>113119.0517</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9128.2341</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Employee Stock Purchase Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">This is a weighted average price.  These shares were sold in multiple transactions on December 11, 2015, inclusive.  The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within this range.</footnote>
        <footnote id="F2">Includes 13,998.3780 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2016 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved; 11,051.3795 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2017 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved; 23,347.3342 shares of Class A Common Stock which vest on July 1, 2018 if the performance criterion described in the applicable Stock Incentive Agreement is achieved; and 12,531.12 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2018 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Noel W. White</signatureName>
        <signatureDate>2015-12-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2015-12-11
0
0000100493
TYSON FOODS INC
TSN
0001340962
White Noel W
2200 DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
President Poultry
Class A Common Stock
2015-12-11
4
S
0
12500
52.48
D
113119.0517
D
Class A Common Stock
9128.2341
I
Employee Stock Purchase Plan
This is a weighted average price.  These shares were sold in multiple transactions on December 11, 2015, inclusive.  The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within this range.
Includes 13,998.3780 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2016 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved; 11,051.3795 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2017 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved; 23,347.3342 shares of Class A Common Stock which vest on July 1, 2018 if the performance criterion described in the applicable Stock Incentive Agreement is achieved; and 12,531.12 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2018 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved.
/s/ Noel W. White
2015-12-15