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

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    <periodOfReport>2016-03-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001592292</rptOwnerCik>
            <rptOwnerName>Carper Howell P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 DON TYSON PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SPRINGDALE</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72762</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP Strategy and New Ventures</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
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                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
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                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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                <transactionAcquiredDisposedCode>
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        <nonDerivativeTransaction>
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            <transactionDate>
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                <transactionAcquiredDisposedCode>
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                <transactionCode>S</transactionCode>
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                <transactionPricePerShare>
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                    <value>D</value>
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        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
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            <transactionDate>
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            </transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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                <sharesOwnedFollowingTransaction>
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            <ownershipNature>
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                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Employee Stock Purchase Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>19.36</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-04-20</value>
            </transactionDate>
            <transactionCoding>
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                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>12100</value>
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                <transactionPricePerShare>
                    <value>19.36</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2013-11-26</value>
            </exerciseDate>
            <expirationDate>
                <value>2022-11-26</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12100.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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                    <value>D</value>
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        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
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                <value>31.82</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-04-20</value>
            </transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>24833</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.82</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <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>24833.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                    <value>24833</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
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                <value>42.26</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-04-20</value>
            </transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>27830</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>42.26</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2015-11-21</value>
            </exerciseDate>
            <expirationDate>
                <value>2024-11-21</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>27830.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>55660</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 9,325.762 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 metrics described in the applicable Stock Incentive Agreement are achieved; includes 7,805.220 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 metrics described in the applicable Stock Incentive Agreement are achieved; and, includes 8,475.039 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">On March 22, 2016, the Reporting Person placed an order with his broker to exercise outstanding options to purchase 64,763 shares of the Issuer's Class A Common Stock and sell said shares if the market price decreased to $64.00 per share, which occurred on the transaction date reported herein.</footnote>
        <footnote id="F4">This is a weighted average price.  These shares were sold in multiple transactions on April 20, 2016 at prices ranging from $63.61 to $63.95, inclusive.  The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within this range.</footnote>
        <footnote id="F5">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/ Howell P. Carper</signatureName>
        <signatureDate>2016-04-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2016-03-17
0
0000100493
TYSON FOODS INC
TSN
0001592292
Carper Howell P
2200 DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
EVP Strategy and New Ventures
Class A Common Stock
2016-03-17
4
J
0
128.6015
0
A
52783.468
D
Class A Common Stock
2016-04-20
4
M
0
12100
19.36
A
64883.468
D
Class A Common Stock
2016-04-20
4
M
0
24833
31.82
A
89716.468
D
Class A Common Stock
2016-04-20
4
M
0
27830
42.26
A
117546.468
D
Class A Common Stock
2016-04-20
4
S
0
64763
63.765
D
52783.468
D
Class A Common Stock
2016-04-21
4
J
0
301.4448
0
A
6318.9377
I
Employee Stock Purchase Plan
Non-Qualified Stock Options (Right to Buy)
19.36
2016-04-20
4
M
0
12100
19.36
D
2013-11-26
2022-11-26
Class A Common Stock
12100.0
0
D
Non-Qualified Stock Options (Right to Buy)
31.82
2016-04-20
4
M
0
24833
31.82
D
2014-11-22
2023-11-22
Class A Common Stock
24833.0
24833
D
Non-Qualified Stock Options (Right to Buy)
42.26
2016-04-20
4
M
0
27830
42.26
D
2015-11-21
2024-11-21
Class A Common Stock
27830.0
55660
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 9,325.762 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 metrics described in the applicable Stock Incentive Agreement are achieved; includes 7,805.220 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 metrics described in the applicable Stock Incentive Agreement are achieved; and, includes 8,475.039 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.
On March 22, 2016, the Reporting Person placed an order with his broker to exercise outstanding options to purchase 64,763 shares of the Issuer's Class A Common Stock and sell said shares if the market price decreased to $64.00 per share, which occurred on the transaction date reported herein.
This is a weighted average price.  These shares were sold in multiple transactions on April 20, 2016 at prices ranging from $63.61 to $63.95, inclusive.  The Reporting Person undertakes to provide to the Issuer, any security holder of the Issuer, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within this range.
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/ Howell P. Carper
2016-04-22