<?xml version="1.0"?>
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        <issuerName>TYSON FOODS INC</issuerName>
        <issuerTradingSymbol>TSN</issuerTradingSymbol>
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            <rptOwnerName>Hayes Thomas P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 W. DON TYSON PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SPRINGDALE</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72762</rptOwnerZipCode>
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            <isOfficer>1</isOfficer>
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            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
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    <derivativeTable>
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                <value>Non-Qualified Stock Options (Right to Buy)</value>
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            <transactionDate>
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                <equitySwapInvolved>0</equitySwapInvolved>
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                    <value>42.26</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            </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>
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            <transactionDate>
                <value>2017-12-19</value>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
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            <transactionAmounts>
                <transactionShares>
                    <value>12254</value>
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                <transactionPricePerShare>
                    <value>50</value>
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                <transactionAcquiredDisposedCode>
                    <value>D</value>
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            <exerciseDate>
                <value>2016-11-30</value>
            </exerciseDate>
            <expirationDate>
                <value>2025-11-30</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>12254.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>24505</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
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            <conversionOrExercisePrice>
                <value>58.34</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-12-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>14749</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>58.34</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</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>
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                <underlyingSecurityShares>
                    <value>14749.0</value>
                </underlyingSecurityShares>
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                <sharesOwnedFollowingTransaction>
                    <value>73739</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents a disposition of shares exempt from Section 16 concurrent reporting requirements pursuant to Rule 16a-12.</footnote>
        <footnote id="F2">Includes 47,814.9497 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; 8,634.783 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; 20,644.945 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 17,634.988 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">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="F4">Includes 47,991.9537 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; 8,666.748 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; 20,721.37 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 17,634.988 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="F5">This is a weighted average price.  These shares were sold in multiple transactions on December 19, 2017 at prices ranging from $81.50 to $81.71, 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="F6">This is a weighted average price.  These shares were sold in multiple transactions on December 19, 2017 at prices ranging from $81.69 to $81.78, 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>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by Power of Attorney for Thomas P. Hayes</signatureName>
        <signatureDate>2017-12-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-11-28
0
0000100493
TYSON FOODS INC
TSN
0001552992
Hayes Thomas P
2200 W. DON TYSON PARKWAY
SPRINGDALE
AR
72762
1
1
0
0
President and CEO
Class A Common Stock
2017-11-28
4
J
0
8581
0
D
103309.6523
D
Class A Common Stock
2017-12-18
4
J
0
285.394
0
A
103595.0463
D
Class A Common Stock
2017-12-19
4
M
0
41745
42.26
A
145340.0463
D
Class A Common Stock
2017-12-19
4
M
0
12254
50
A
157594.0463
D
Class A Common Stock
2017-12-19
4
M
0
14749
58.34
A
172343.0463
D
Class A Common Stock
2017-12-19
4
S
0
31454
81.564
D
140889.0463
D
Class A Common Stock
2017-12-19
4
S
0
9829
81.721
D
131060.0463
D
Class A Common Stock
2017-12-19
4
S
0
12591
81.714
D
118469.0463
D
Class A Common Stock
2017-12-20
4
J
0
14874
0
D
103595.0463
D
Non-Qualified Stock Options (Right to Buy)
42.26
2017-12-19
4
M
0
41745
42.26
D
2015-11-21
2024-11-21
Class A Common Stock
41745.0
41745
D
Non-Qualified Stock Options (Right to Buy)
50.0
2017-12-19
4
M
0
12254
50
D
2016-11-30
2025-11-30
Class A Common Stock
12254.0
24505
D
Non-Qualified Stock Options (Right to Buy)
58.34
2017-12-19
4
M
0
14749
58.34
D
2017-11-28
2026-11-28
Class A Common Stock
14749.0
73739
D
Represents a disposition of shares exempt from Section 16 concurrent reporting requirements pursuant to Rule 16a-12.
Includes 47,814.9497 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; 8,634.783 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; 20,644.945 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 17,634.988 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.
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 47,991.9537 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; 8,666.748 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; 20,721.37 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 17,634.988 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.
This is a weighted average price.  These shares were sold in multiple transactions on December 19, 2017 at prices ranging from $81.50 to $81.71, 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.
This is a weighted average price.  These shares were sold in multiple transactions on December 19, 2017 at prices ranging from $81.69 to $81.78, 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.
/s/ R. Read Hudson by Power of Attorney for Thomas P. Hayes
2017-12-20