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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-09-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001703544</rptOwnerCik>
            <rptOwnerName>Ramsey Douglas Wayne</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 W 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>Group President Poultry</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2017-09-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>109.476</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>15747.5588</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>2017-09-30</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>0.6675</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>96.0012</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>2017-11-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>5450.814</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21198.3728</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Non-Qualified Stock Options (Right to Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>77.97</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-11-17</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>23314</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>77.97</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2018-11-17</value>
            </exerciseDate>
            <expirationDate>
                <value>2027-11-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>23314.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>23314</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Shares</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F5"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2017-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>21803.258</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>21803.258</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21803.258</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 2,187.5518 shares of Class A Common Stock which vest on November 21, 2017; 1,534.374 shares of Class A Common Stock which vest on November 30, 2018 and 1,305.504 shares of Class A Common Stock which vest on November 18, 2019.</footnote>
        <footnote id="F3">Award of Class A Common Stock which vests on November 13, 2020 if the performance metric described in the applicable Stock Incentive Agreement (the Incentive Agreement) are achieved and the Reporting Person is employed by the Issuer on the vesting date. The performance metrics are achievement of a three year (fiscal 2018-2020) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metric is not achieved, the award expires.</footnote>
        <footnote id="F4">The stock options vest at 33 1/3% on each of the first, second, and third anniversary dates of the grant.</footnote>
        <footnote id="F5">Award of performance Class A Common Stock which vests on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved. The performance criteria set forth in the Stock Incentive Agreement are (1) achievement of a three year (fiscal 2018-2020) cumulative EBIT 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 2018-2020 ) period. Subject to the achievement of the performance criteria, the performance shares could vest at a level of 50 percent to 200 percent and are reported as derivative securities at the 200 percent level. If neither of the performance criteria is achieved, the award expires.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Douglas W. Ramsey</signatureName>
        <signatureDate>2017-11-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-09-19
0
0000100493
TYSON FOODS INC
TSN
0001703544
Ramsey Douglas Wayne
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
Group President Poultry
Class A Common Stock
2017-09-19
4
J
0
109.476
0
A
15747.5588
D
Class A Common Stock
2017-09-30
4
J
0
0.6675
0
A
96.0012
I
Employee Stock Purchase Plan
Class A Common Stock
2017-11-17
4
A
0
5450.814
0
A
21198.3728
D
Non-Qualified Stock Options (Right to Buy)
77.97
2017-11-17
4
A
0
23314
77.97
A
2018-11-17
2027-11-17
Class A Common Stock
23314.0
23314
D
Performance Shares
2017-11-21
4
A
0
21803.258
A
Class A Common Stock
21803.258
21803.258
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 2,187.5518 shares of Class A Common Stock which vest on November 21, 2017; 1,534.374 shares of Class A Common Stock which vest on November 30, 2018 and 1,305.504 shares of Class A Common Stock which vest on November 18, 2019.
Award of Class A Common Stock which vests on November 13, 2020 if the performance metric described in the applicable Stock Incentive Agreement (the Incentive Agreement) are achieved and the Reporting Person is employed by the Issuer on the vesting date. The performance metrics are achievement of a three year (fiscal 2018-2020) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metric is not achieved, the award expires.
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 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved. The performance criteria set forth in the Stock Incentive Agreement are (1) achievement of a three year (fiscal 2018-2020) cumulative EBIT 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 2018-2020 ) period. Subject to the achievement of the performance criteria, the performance shares could vest at a level of 50 percent to 200 percent and are reported as derivative securities at the 200 percent level. If neither of the performance criteria is achieved, the award expires.
/s/ Douglas W. Ramsey
2017-11-21