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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-06-20</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001415534</rptOwnerCik>
            <rptOwnerName>King Donnie</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 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>Pres North American Operations</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

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            <transactionDate>
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                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>171135.29</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
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            <transactionDate>
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            <transactionAmounts>
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                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                <sharesOwnedFollowingTransaction>
                    <value>221442.29</value>
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                <directOrIndirectOwnership>
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        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
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            <transactionDate>
                <value>2016-08-25</value>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-08-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
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            <transactionAmounts>
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                    <value>754.427</value>
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                <transactionAcquiredDisposedCode>
                    <value>A</value>
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                <sharesOwnedFollowingTransaction>
                    <value>13271.113</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Employee Stock Purchase Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
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                <sharesOwnedFollowingTransaction>
                    <value>950</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Joint IRA</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
            </securityTitle>
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                <value>31.82</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-08-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>96334</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.82</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2014-11-22</value>
            </exerciseDate>
            <expirationDate>
                <value>2023-11-22</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>96334.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>48166</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
            </securityTitle>
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                <value>42.26</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-08-25</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>50307</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.26</value>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <exerciseDate>
                <value>2015-11-21</value>
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            <expirationDate>
                <value>2024-11-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>50307.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100614</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 18,133.716 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2016 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved; 14,144.636 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2017 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved; 23,523.499 shares of Class A Common Stock which vest on July 1, 2018 if the performance criterion described in the applicable Stock Incentive Agreement is achieved; and 23,619.599 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved.</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>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson as Power of Attorney for Donnie King</signatureName>
        <signatureDate>2016-08-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2016-06-20
0
0000100493
TYSON FOODS INC
TSN
0001415534
King Donnie
2200 DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
Pres North American Operations
Class A Common Stock
2016-06-20
4
J
0
648.1058
0
A
171135.29
D
Class A Common Stock
2016-08-25
4
M
0
96334
31.82
A
267469.29
D
Class A Common Stock
2016-08-25
4
S
0
96334
75.75
D
171135.29
D
Class A Common Stock
2016-08-25
4
M
0
50307
42.26
A
221442.29
D
Class A Common Stock
2016-08-25
4
S
0
50307
75.75
D
171135.29
D
Class A Common Stock
2016-08-25
4
J
0
754.427
0
A
13271.113
I
Employee Stock Purchase Plan
Class A Common Stock
950
I
Joint IRA
Non-Qualified Stock Options (Right to Buy)
31.82
2016-08-25
4
M
0
96334
31.82
D
2014-11-22
2023-11-22
Class A Common Stock
96334.0
48166
D
Non-Qualified Stock Options (Right to Buy)
42.26
2016-08-25
4
M
0
50307
42.26
D
2015-11-21
2024-11-21
Class A Common Stock
50307.0
100614
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 18,133.716 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2016 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved; 14,144.636 shares of Class A Common Stock which vest on the fourth business day following the filing of the Issuer's Annual Report on Form 10-K for its 2017 fiscal year if the performance criterion described in the applicable Stock Incentive Agreement is achieved; 23,523.499 shares of Class A Common Stock which vest on July 1, 2018 if the performance criterion described in the applicable Stock Incentive Agreement is achieved; and 23,619.599 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved.
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.
/s/ R. Read Hudson as Power of Attorney for Donnie King
2016-08-26