<?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>0001497610</rptOwnerCik>
            <rptOwnerName>Oleksiuk Mary</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>400 S. JEFFERSON STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60607</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP &amp; Chief HR Officer</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>797.564</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>58289.8557</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>2018-11-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1154.3122</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2708.6202</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>2018-11-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
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            <transactionAmounts>
                <transactionShares>
                    <value>7152.474</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>65442.3297</value>
                    <footnoteId id="F5"/>
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            <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="F6"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>37445</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>37445.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>37445</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>2018-11-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>28609.896</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>28609.896</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>28609.896</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 10,411.81 shares of Class A Common Stock which vest on December 1, 2018 if the performance metric described in the applicable Stock Incentive Agreement (the &quot;SIA&quot;) is achieved; 7,477.704 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable SIA is achieved; 25,166.026 shares of Class A Common Stock which vest on February 15, 2020 if the performance metric described in the applicable SIA is achieved; and 5,235.773 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is 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>
        <footnote id="F4">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="F5">Includes 10,411.81 shares of Class A Common Stock which vest on December 1, 2018 if the performance metric described in the applicable SIA is achieved; 7,477.704 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable SIA is achieved; 25,166.026 shares of Class A Common Stock which vest on February 15, 2020 if the performance metric described in the applicable SIA is achieved; 5,235.773 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved; and 7,152.474 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="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 29, 2021 if the performance metrics described in the 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 Mary Oleksiuk</signatureName>
        <signatureDate>2018-11-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-09-18
0
0000100493
TYSON FOODS INC
TSN
0001497610
Oleksiuk Mary
400 S. JEFFERSON STREET
CHICAGO
IL
60607
0
1
0
0
EVP & Chief HR Officer
Class A Common Stock
2018-09-18
4
J
0
797.564
0
A
58289.8557
D
Class A Common Stock
2018-11-15
4
J
0
1154.3122
0
A
2708.6202
I
Employee Stock Purchase Plan
Class A Common Stock
2018-11-19
4
A
0
7152.474
0
A
65442.3297
D
Non-Qualified Stock Options (Right to Buy)
59.42
2018-11-19
4
A
0
37445
59.42
A
2019-11-19
2028-11-19
Class A Common Stock
37445.0
37445
D
Performance Shares
2018-11-19
4
A
0
28609.896
A
Class A Common Stock
28609.896
28609.896
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 10,411.81 shares of Class A Common Stock which vest on December 1, 2018 if the performance metric described in the applicable Stock Incentive Agreement (the "SIA") is achieved; 7,477.704 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable SIA is achieved; 25,166.026 shares of Class A Common Stock which vest on February 15, 2020 if the performance metric described in the applicable SIA is achieved; and 5,235.773 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is 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.
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 10,411.81 shares of Class A Common Stock which vest on December 1, 2018 if the performance metric described in the applicable SIA is achieved; 7,477.704 shares of Class A Common Stock which vest on November 18, 2019 if the performance metric described in the applicable SIA is achieved; 25,166.026 shares of Class A Common Stock which vest on February 15, 2020 if the performance metric described in the applicable SIA is achieved; 5,235.773 shares of Class A Common Stock which vest on November 13, 2020 if the performance metric described in the applicable SIA is achieved; and 7,152.474 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 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 Mary Oleksiuk
2018-11-21