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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-12-19</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>Chief HR Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>78.0637</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21646.2937</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>2017-02-09</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>252.7976</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>648.1934</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>2017-02-15</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>24491.045</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>65.33</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>46137.3387</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></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 4,236.5957 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 (SIA) are achieved; 10,132.554 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; and 7,277.144 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA 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>
        <footnote id="F4">Award of Class A Common Stock which vests on February 14, 2020 if the performance metric described in the applicable Stock Incentive Agreement (SIA) are achieved and the Reporting Person is employed by the Issuer on the vesting date. The performance metrics are achievement of a two year (fiscal 2018-2019) cumulative EBIT target as set forth in the SIA. If the performance metrics are not achieved, the award expires.</footnote>
        <footnote id="F5">Includes 4,236.5957 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 SIA are achieved; 10,132.554 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; 7,277.144 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; and 24,491.045 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved and the Reporting Person is employed by the Issuer on the vesting date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by Power of Attorney for Mary Oleksiuk</signatureName>
        <signatureDate>2017-02-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2016-12-19
0
0000100493
TYSON FOODS INC
TSN
0001497610
Oleksiuk Mary
400 S. JEFFERSON STREET
CHICAGO
IL
60607
0
1
0
0
Chief HR Officer
Class A Common Stock
2016-12-19
4
J
0
78.0637
0
A
21646.2937
D
Class A Common Stock
2017-02-09
4
J
0
252.7976
0
A
648.1934
I
Employee Stock Purchase Plan
Class A Common Stock
2017-02-15
4
A
0
24491.045
65.33
A
46137.3387
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 4,236.5957 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 (SIA) are achieved; 10,132.554 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; and 7,277.144 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA 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.
Award of Class A Common Stock which vests on February 14, 2020 if the performance metric described in the applicable Stock Incentive Agreement (SIA) are achieved and the Reporting Person is employed by the Issuer on the vesting date. The performance metrics are achievement of a two year (fiscal 2018-2019) cumulative EBIT target as set forth in the SIA. If the performance metrics are not achieved, the award expires.
Includes 4,236.5957 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 SIA are achieved; 10,132.554 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; 7,277.144 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; and 24,491.045 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved and the Reporting Person is employed by the Issuer on the vesting date.
/s/ R. Read Hudson by Power of Attorney for Mary Oleksiuk
2017-02-17