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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-11-30</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>Group President Poultry</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-11-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>489</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27532.7088</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>2018-12-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5707.80</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>33240.5088</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>2018-12-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1785</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>31455.5088</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>97.6128</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="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-12-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>6000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>6000.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On November 30, 2015, the Reporting Person received a grant of 1,500 shares which, with reinvested dividends, vested on November 30, 2018. This grant has previously been reported as beneficially owned by the Reporting Person. Pursuant to an election made by the Reporting Person, 489 shares were sold by the Reporting Person to the Issuer on November 30, 2018, to satisfy tax withholding obligations.</footnote>
        <footnote id="F2">Includes 1,325.78 shares of Class A Common Stock which vest on November 18, 2019; 10,900.084 shares of Class A Common Stock which vest on May 12, 2020 if the performance metric described in the applicable Stock Incentive Agreement (&quot;SIA&quot;) is achieved; 5,542.315 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved; and 7,573.208 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">On November 30, 2015 the Reporting Person received a grant of 3,000 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, 5,707.8 shares vested and are reported herein as acquired non-derivatives securities and 292.2 shares expired.</footnote>
        <footnote id="F4">Pursuant to an election made by the Reporting Person, 1,785 shares were sold by the Reporting Person to the Issuer on December 1, 2018, to satisfy tax withholding obligations related to the vesting described in footnote 3.</footnote>
        <footnote id="F5">A portion of these performance shares vested as described in footnote 3. The remainder of the award expired.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson as Power of Attorney for Douglas W. Ramsey</signatureName>
        <signatureDate>2018-12-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-11-30
0
0000100493
TYSON FOODS INC
TSN
0001703544
Ramsey Douglas Wayne
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
Group President Poultry
Class A Common Stock
2018-11-30
4
F
0
489
0
D
27532.7088
D
Class A Common Stock
2018-12-01
4
M
0
5707.80
0
A
33240.5088
D
Class A Common Stock
2018-12-01
4
F
0
1785
0
D
31455.5088
D
Class A Common Stock
97.6128
I
Employee Stock Purchase Plan
Performance Shares
2018-12-01
4
M
0
6000
0
D
Class A Common Stock
6000.0
0
D
On November 30, 2015, the Reporting Person received a grant of 1,500 shares which, with reinvested dividends, vested on November 30, 2018. This grant has previously been reported as beneficially owned by the Reporting Person. Pursuant to an election made by the Reporting Person, 489 shares were sold by the Reporting Person to the Issuer on November 30, 2018, to satisfy tax withholding obligations.
Includes 1,325.78 shares of Class A Common Stock which vest on November 18, 2019; 10,900.084 shares of Class A Common Stock which vest on May 12, 2020 if the performance metric described in the applicable Stock Incentive Agreement ("SIA") is achieved; 5,542.315 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved; and 7,573.208 shares of Class A Common Stock which vest on November 29, 2021 if the performance metric described in the applicable SIA is achieved.
On November 30, 2015 the Reporting Person received a grant of 3,000 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, 5,707.8 shares vested and are reported herein as acquired non-derivatives securities and 292.2 shares expired.
Pursuant to an election made by the Reporting Person, 1,785 shares were sold by the Reporting Person to the Issuer on December 1, 2018, to satisfy tax withholding obligations related to the vesting described in footnote 3.
A portion of these performance shares vested as described in footnote 3. The remainder of the award expired.
/s/ R. Read Hudson as Power of Attorney for Douglas W. Ramsey
2018-12-04