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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-11-17</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>2017-11-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3847.634</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21887.6708</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>77.97</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-11-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>16457</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>77.97</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2018-11-17</value>
            </exerciseDate>
            <expirationDate>
                <value>2027-11-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>16457.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                    <value>16457</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F4"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>15390.534</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>15390.534</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15390.534</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Award of Class A Common Stock which vests on November 13, 2020 if the performance metric described in the applicable Stock Incentive Agreement (the Incentive Agreement) are achieved and the Reporting Person is employed by the Issuer on the vesting date. The performance metrics are achievement of a three year (fiscal 2018-2020) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metric is not achieved, the award expires.</footnote>
        <footnote id="F2">Includes 2,187.5518 shares of Class A Common Stock which vest on November 21, 2017; 1,538.11 shares of Class A Common Stock which vest on November 30, 2018; 1,736.398 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>
        <footnote id="F3">The stock options vest at 33 1/3% on each of the first, second, and third anniversary dates of the grant.</footnote>
        <footnote id="F4">Award of performance Class A Common Stock which vests on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved. The performance criteria set forth in the Stock Incentive Agreement are (1) achievement of a three year (fiscal 2018-2020) cumulative EBIT target and (2) a favorable comparison of the relative total shareholder return of the Issuer's Class A Common Stock compared to a predetermined peer group of publicly traded companies over a three year (fiscal 2018-2020 ) period. Subject to the achievement of the performance criteria, the performance shares could vest at a level of 50 percent to 200 percent and are reported as derivative securities at the 200 percent level. If neither of the performance criteria is achieved, the award expires.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Scott Rouse</signatureName>
        <signatureDate>2017-11-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-11-17
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
2017-11-17
4
A
0
3847.634
0
A
21887.6708
D
Non-Qualified Stock Options (Right to Buy)
77.97
2017-11-17
4
A
0
16457
77.97
A
2018-11-17
2027-11-17
Class A Common Stock
16457.0
16457
D
Performance Shares
2017-11-21
4
A
0
15390.534
A
Class A Common Stock
15390.534
15390.534
D
Award of Class A Common Stock which vests on November 13, 2020 if the performance metric described in the applicable Stock Incentive Agreement (the Incentive Agreement) are achieved and the Reporting Person is employed by the Issuer on the vesting date. The performance metrics are achievement of a three year (fiscal 2018-2020) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metric is not achieved, the award expires.
Includes 2,187.5518 shares of Class A Common Stock which vest on November 21, 2017; 1,538.11 shares of Class A Common Stock which vest on November 30, 2018; 1,736.398 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.
The stock options vest at 33 1/3% on each of the first, second, and third anniversary dates of the grant.
Award of performance Class A Common Stock which vests on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved. The performance criteria set forth in the Stock Incentive Agreement are (1) achievement of a three year (fiscal 2018-2020) cumulative EBIT target and (2) a favorable comparison of the relative total shareholder return of the Issuer's Class A Common Stock compared to a predetermined peer group of publicly traded companies over a three year (fiscal 2018-2020 ) period. Subject to the achievement of the performance criteria, the performance shares could vest at a level of 50 percent to 200 percent and are reported as derivative securities at the 200 percent level. If neither of the performance criteria is achieved, the award expires.
/s/ Scott Rouse
2017-11-21