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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-11-29</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001557040</rptOwnerCik>
            <rptOwnerName>Calaway Curt</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>SVP Controller &amp; CAO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-11-29</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>31.6675</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4205.4804</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Employee Stock Purchase Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <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="F2"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>489</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21041.413</value>
                    <footnoteId id="F3"/>
                </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="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5707.80</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26749.213</value>
                    <footnoteId id="F3"/>
                </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="F5"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1785</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>24964.213</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F6"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-11-30</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="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </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">Represents shares of the Issuer's Class A Common Stock purchased for the Reporting Person's account under the Issuer's Employee Stock Purchase Plan since the last Statement of Changes in Beneficial Ownership was filed by the Reporting Person.  Such acquisitions are exempt from Section 16 concurrent reporting requirements pursuant to Rule 16b-3.</footnote>
        <footnote id="F2">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="F3">Includes 1,325.78 shares of Class A Common Stock which vest on November 28, 2019; 978.056 shares of Class A Common Stock which vest on November 17, 2020; and 1,262.201 shares of Class A Common Stock which vest on November 29, 2021.</footnote>
        <footnote id="F4">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="F5">Pursuant to an election made by the Reporting Person, 1,785 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations related to the vesting described in footnote 4.</footnote>
        <footnote id="F6">A portion of these performance shares vested as described in footnote 4.  The remainder of the award expired.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by Power of Attorney for Curt Calaway</signatureName>
        <signatureDate>2018-12-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-11-29
0
0000100493
TYSON FOODS INC
TSN
0001557040
Calaway Curt
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
SVP Controller & CAO
Class A Common Stock
2018-11-29
4
J
0
31.6675
0
A
4205.4804
I
Employee Stock Purchase Plan
Class A Common Stock
2018-11-30
4
F
0
489
0
D
21041.413
D
Class A Common Stock
2018-12-01
4
M
0
5707.80
0
A
26749.213
D
Class A Common Stock
2018-12-01
4
F
0
1785
0
D
24964.213
D
Performance Shares
2018-11-30
4
M
0
6000
0
D
Class A Common Stock
6000.0
0
D
Represents shares of the Issuer's Class A Common Stock purchased for the Reporting Person's account under the Issuer's Employee Stock Purchase Plan since the last Statement of Changes in Beneficial Ownership was filed by the Reporting Person.  Such acquisitions are exempt from Section 16 concurrent reporting requirements pursuant to Rule 16b-3.
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 28, 2019; 978.056 shares of Class A Common Stock which vest on November 17, 2020; and 1,262.201 shares of Class A Common Stock which vest on November 29, 2021.
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 to satisfy tax withholding obligations related to the vesting described in footnote 4.
A portion of these performance shares vested as described in footnote 4.  The remainder of the award expired.
/s/ R. Read Hudson by Power of Attorney for Curt Calaway
2018-12-04