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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-11-21</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001698306</rptOwnerCik>
            <rptOwnerName>Rouse Scott</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>Chief Customer Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>789</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21098.6708</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>1685.7254</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">On November 21, 2017, 2,187.5518 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, 789 shares were sold by the Reporting Person to the Issuer on November 21, 2017, to satisfy tax withholding obligations.</footnote>
        <footnote id="F2">Includes 1,535.987 shares of Class A Common Stock which vest on November 30, 2018; 1,738.522 shares of Class A Common Stock which vest on November 18, 2019; 7,750.015 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 3,847.634 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by Power of Attorney for Scott Rouse</signatureName>
        <signatureDate>2017-11-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-11-21
0
0000100493
TYSON FOODS INC
TSN
0001698306
Rouse Scott
2200 W. DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
Chief Customer Officer
Class A Common Stock
2017-11-21
4
F
0
789
0
D
21098.6708
D
Class A Common Stock
1685.7254
I
Employee Stock Purchase Plan
On November 21, 2017, 2,187.5518 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, 789 shares were sold by the Reporting Person to the Issuer on November 21, 2017, to satisfy tax withholding obligations.
Includes 1,535.987 shares of Class A Common Stock which vest on November 30, 2018; 1,738.522 shares of Class A Common Stock which vest on November 18, 2019; 7,750.015 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 3,847.634 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved.
/s/ R. Read Hudson by Power of Attorney for Scott Rouse
2017-11-22