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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-09-15</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>2016-09-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>35.406</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17421.875</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>2016-11-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>169.8413</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2672.0829</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>2016-11-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1285.567</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18707.442</value>
                    <footnoteId id="F5"/>
                </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>58.34</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-11-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F6"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5589</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>58.34</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2017-11-28</value>
            </exerciseDate>
            <expirationDate>
                <value>2026-11-28</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5589.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5589</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F7"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-11-28</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F7"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5142.27</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F7"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5142.27</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5142.27</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 1,514.402 shares of Class A Common Stock which vest on November 30, 2018.</footnote>
        <footnote id="F3">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="F4">Award of Class A Common Stock which vests on November 28, 2019.</footnote>
        <footnote id="F5">Includes 1,514.402 shares of Class A Common Stock which vest on November 30, 2018 and 1,285.567 shares of Class A Common Stock which vest on November 28, 2019.</footnote>
        <footnote id="F6">The stock options vest at 33 1/3% on each of the first, second, and third anniversary dates of the grant.</footnote>
        <footnote id="F7">Award of performance Class A Common Stock which vests on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved. The performance metrics set forth in the Stock Incentive Agreement are (1) achievement of a three year (fiscal 2017-2019) 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 2017-2019) period. Subject to the achievement of the performance metrics, the performance shares could vest at a level of 50%-200% and are reported as derivative securities at the 200% level. If neither of the performance metrics are achieved, the award expires.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Curt Calaway</signatureName>
        <signatureDate>2016-11-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
[{"type": "4", "sequence": "1", "filename": "wf-form4_148054113904219.xml", "description": "FORM 4", "secsgml_size_bytes": 12397}]
X0306
4
2016-09-15
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
2016-09-15
4
J
0
35.406
0
A
17421.875
D
Class A Common Stock
2016-11-17
4
J
0
169.8413
0
A
2672.0829
I
Employee Stock Purchase Plan
Class A Common Stock
2016-11-28
4
A
0
1285.567
0
A
18707.442
D
Non-Qualified Stock Options (Right to Buy)
58.34
2016-11-28
4
A
0
5589
58.34
A
2017-11-28
2026-11-28
Class A Common Stock
5589.0
5589
D
Performance Shares
2016-11-28
4
A
0
5142.27
A
Class A Common Stock
5142.27
5142.27
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 1,514.402 shares of Class A Common Stock which vest on November 30, 2018.
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.
Award of Class A Common Stock which vests on November 28, 2019.
Includes 1,514.402 shares of Class A Common Stock which vest on November 30, 2018 and 1,285.567 shares of Class A Common Stock which vest on November 28, 2019.
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 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved. The performance metrics set forth in the Stock Incentive Agreement are (1) achievement of a three year (fiscal 2017-2019) 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 2017-2019) period. Subject to the achievement of the performance metrics, the performance shares could vest at a level of 50%-200% and are reported as derivative securities at the 200% level. If neither of the performance metrics are achieved, the award expires.
/s/ Curt Calaway
2016-11-30