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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-12-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001019032</rptOwnerCik>
            <rptOwnerName>TYSON JOHN H</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>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman of the Board</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-12-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
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            <transactionAmounts>
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                    <value>95323.437</value>
                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2571855.1855</value>
                    <footnoteId id="F2"/>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
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            <transactionDate>
                <value>2018-12-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>40668</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
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                    <value>2531187.1855</value>
                    <footnoteId id="F4"/>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
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            <transactionDate>
                <value>2018-12-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
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            <transactionAmounts>
                <transactionShares>
                    <value>11128</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2520059.1855</value>
                    <footnoteId id="F4"/>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>118423.9762</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Employee Stock Purchase Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F6"/>
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            <transactionDate>
                <value>2018-12-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>100203.34</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>100203.34</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On November 30, 2015 the Reporting Person received a grant of 50,101.5 performance shares which vested or expired on December 1, 2018 subject to the achievement of performance criteria in the applicable Stock Incentive Agreement. The performance criteria were (a) a cumulative adjusted earnings before interest and taxes (EBIT) target of $6,877 million for the 2016-2018 fiscal years and (b) a favorable comparison of the Issuer's Class A common stock price relative to the stock prices of a predetermined peer group of publicly traded companies over the 2016-2018 fiscal years. The performance shares could vest at a level of 50%-200% and were previously reported as derivative securities at the 200% level. On December 1, 2018, 95,323.437 shares vested and are reported herein as acquired non-derivatives securities and 4,879.563 shares expired.</footnote>
        <footnote id="F2">Includes 26,082.455 shares of Class A Common Stock which vested on December 1, 2018 as described in footnote 5; 22,141.254 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable Stock Incentive Agreement (&quot;SIA&quot;) is achieved; 17,115.974 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved; and 24,402.558 shares of Class A Common Stock which vest on November 29, 2021 if the performance metric described in the applicable SIA is achieved.</footnote>
        <footnote id="F3">Pursuant to an election made by the Reporting Person, 40,668 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations related to the vesting described in footnote 1.</footnote>
        <footnote id="F4">Includes 22,141.254 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable SIA is achieved; 17,115.974 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved; and 24,402.558 shares of Class A Common Stock which vest on November 29, 2021 if the performance metric described in the applicable SIA is achieved.</footnote>
        <footnote id="F5">On December 1, 2018, 26,082.455 shares of restricted Class A Common Stock vested. These shares were previously reported as beneficially owned by the Reporting Person. Pursuant to an election made by the Reporting Person, 11,128 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations.</footnote>
        <footnote id="F6">A portion of these performance shares vested as described in footnote 1. The remainder of the award expired.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by Power of Attorney for John H. Tyson</signatureName>
        <signatureDate>2018-12-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-12-01
0
0000100493
TYSON FOODS INC
TSN
0001019032
TYSON JOHN H
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
1
1
0
0
Chairman of the Board
Class A Common Stock
2018-12-01
4
M
0
95323.437
0
A
2571855.1855
D
Class A Common Stock
2018-12-01
4
F
0
40668
0
D
2531187.1855
D
Class A Common Stock
2018-12-01
4
F
0
11128
0
D
2520059.1855
D
Class A Common Stock
118423.9762
I
Employee Stock Purchase Plan
Performance Shares
2018-12-01
4
M
0
100203.34
0
D
Class A Common Stock
100203.34
0
D
On November 30, 2015 the Reporting Person received a grant of 50,101.5 performance shares which vested or expired on December 1, 2018 subject to the achievement of performance criteria in the applicable Stock Incentive Agreement. The performance criteria were (a) a cumulative adjusted earnings before interest and taxes (EBIT) target of $6,877 million for the 2016-2018 fiscal years and (b) a favorable comparison of the Issuer's Class A common stock price relative to the stock prices of a predetermined peer group of publicly traded companies over the 2016-2018 fiscal years. The performance shares could vest at a level of 50%-200% and were previously reported as derivative securities at the 200% level. On December 1, 2018, 95,323.437 shares vested and are reported herein as acquired non-derivatives securities and 4,879.563 shares expired.
Includes 26,082.455 shares of Class A Common Stock which vested on December 1, 2018 as described in footnote 5; 22,141.254 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable Stock Incentive Agreement ("SIA") is achieved; 17,115.974 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved; and 24,402.558 shares of Class A Common Stock which vest on November 29, 2021 if the performance metric described in the applicable SIA is achieved.
Pursuant to an election made by the Reporting Person, 40,668 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations related to the vesting described in footnote 1.
Includes 22,141.254 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable SIA is achieved; 17,115.974 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved; and 24,402.558 shares of Class A Common Stock which vest on November 29, 2021 if the performance metric described in the applicable SIA is achieved.
On December 1, 2018, 26,082.455 shares of restricted Class A Common Stock vested. These shares were previously reported as beneficially owned by the Reporting Person. Pursuant to an election made by the Reporting Person, 11,128 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations.
A portion of these performance shares vested as described in footnote 1. The remainder of the award expired.
/s/ R. Read Hudson by Power of Attorney for John H. Tyson
2018-12-04