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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-09-18</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001725741</rptOwnerCik>
            <rptOwnerName>Tu Amy</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>EVP &amp; General Counsel</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-09-18</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>48.118</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3739.063</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>2018-11-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5890.273</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>9629.336</value>
                    <footnoteId id="F4"/>
                </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>59.42</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-11-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F5"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>30838</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>59.42</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2019-11-19</value>
            </exerciseDate>
            <expirationDate>
                <value>2028-11-19</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>30838.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>30838</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F6"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2018-11-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>23561.09</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F6"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F6"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>23561.09</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>23561.09</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 received by the Reporting Person pursuant to the Issuer's dividend reinvestment 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 16a-11.</footnote>
        <footnote id="F2">Includes 3,739.063 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable Stock Incentive Agreement (the &quot;SIA&quot;) is achieved.</footnote>
        <footnote id="F3">Award of Class A Common Stock which vests on November 29, 2021 if the performance metric described in the applicable SIA is achieved. The performance metric is the achievement of a three year (fiscal 2019-2021) cumulative adjusted operating income target as set forth in the SIA. If the performance metric is not achieved, the award expires.</footnote>
        <footnote id="F4">Includes 3,739.063 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved and 5,890.273 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">The stock options vest at 33 1/3% on each of the first, second, and third anniversary dates of the grant.</footnote>
        <footnote id="F6">Award of performance Class A Common Stock which vests on November 29, 2021 if the performance metrics described in the applicable SIA are achieved. The performance metrics set forth in the SIA are (1) achievement of a three year (fiscal 2019-2021) cumulative operating income 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 2019-2021) period. Subject to the achievement of the performance metrics, the performance shares could vest at a level of 50 to 200 percent and are reported as derivative securities at the 200 percent level. If neither of the performance metrics are achieved, the award expires.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by Power of Attorney for Amy Tu</signatureName>
        <signatureDate>2018-11-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-09-18
0
0000100493
TYSON FOODS INC
TSN
0001725741
Tu Amy
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
EVP & General Counsel
Class A Common Stock
2018-09-18
4
J
0
48.118
0
A
3739.063
D
Class A Common Stock
2018-11-19
4
A
0
5890.273
0
A
9629.336
D
Non-Qualified Stock Options (Right to Buy)
59.42
2018-11-19
4
A
0
30838
59.42
A
2019-11-19
2028-11-19
Class A Common Stock
30838.0
30838
D
Performance Shares
2018-11-19
4
A
0
23561.09
A
Class A Common Stock
23561.09
23561.09
D
Represents shares of the Issuer's Class A Common Stock received by the Reporting Person pursuant to the Issuer's dividend reinvestment 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 16a-11.
Includes 3,739.063 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable Stock Incentive Agreement (the "SIA") is achieved.
Award of Class A Common Stock which vests on November 29, 2021 if the performance metric described in the applicable SIA is achieved. The performance metric is the achievement of a three year (fiscal 2019-2021) cumulative adjusted operating income target as set forth in the SIA. If the performance metric is not achieved, the award expires.
Includes 3,739.063 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved and 5,890.273 shares of Class A Common Stock which vest on November 29, 2021 if the performance metric described in the applicable SIA is 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 29, 2021 if the performance metrics described in the applicable SIA are achieved. The performance metrics set forth in the SIA are (1) achievement of a three year (fiscal 2019-2021) cumulative operating income 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 2019-2021) period. Subject to the achievement of the performance metrics, the performance shares could vest at a level of 50 to 200 percent and are reported as derivative securities at the 200 percent level. If neither of the performance metrics are achieved, the award expires.
/s/ R. Read Hudson by Power of Attorney for Amy Tu
2018-11-21