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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-12-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001105965</rptOwnerCik>
            <rptOwnerName>KEVER JIM D</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2200 DON TYSON PARKWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SPRINGDALE</rptOwnerCity>
            <rptOwnerState>AR</rptOwnerState>
            <rptOwnerZipCode>72762</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2013-12-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>419</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>68395</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>2014-01-31</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3342</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>71737</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-02-03</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.03</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>74737</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2800</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>by spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>17.03</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2014-02-03</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>M</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.03</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2006-02-06</value>
            </exerciseDate>
            <expirationDate>
                <value>2014-02-06</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>3000.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of the Issuers Class A Common Stock received by the Reporting Person pursuant to a dividend reinvestment feature under the Issuer's stock plan since the last Statement of Changes in Beneficial Ownership was filed by the Reporting Person. Such acquisitions are exempt from Section 16 reporting requirements pursuant to Rule 16a-11.</footnote>
        <footnote id="F2">Includes 52,903 shares of the Issuer's Class A Common Stock acquired by the Reporting Person pursuant to the Deferred Fee Plan for Directors, which shares shall vest 180 days after termination of the Reporting Person's service as a member of the Issuer's board of directors.</footnote>
        <footnote id="F3">Represents a stock award for shares of the Issuer's Class A Common Stock having a value of $125,000 granted on the date of election as a director at the 2014 Annual Meeting of Shareholders (January 31, 2014). Per the Deferred Fee Plan for Directors, these shares shall vest 180 days after termination of the Reporting Person's service as a member of the Issuer's board of directors.</footnote>
        <footnote id="F4">Includes 56,245 shares of the Issuer's Class A Common Stock acquired by the Reporting Person pursuant to the Deferred Fee Plan for Directors, which shares shall vest 180 days after termination of the Reporting Person's service as a member of the Issuer's board of directors.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ R. Read Hudson by power of Attorney for Jim D. Kever</signatureName>
        <signatureDate>2014-02-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2013-12-16
0
0000100493
TYSON FOODS INC
TSN
0001105965
KEVER JIM D
2200 DON TYSON PARKWAY
SPRINGDALE
AR
72762
1
0
0
0
Class A Common Stock
2013-12-16
4
J
0
419
0
A
68395
D
Class A Common Stock
2014-01-31
4
J
0
3342
0
A
71737
D
Class A Common Stock
2014-02-03
4
M
0
3000
17.03
A
74737
D
Class A Common Stock
2800
I
by spouse
Class A Common Stock
17.03
2014-02-03
4
M
0
3000
17.03
D
2006-02-06
2014-02-06
Class A Common Stock
3000.0
0
D
Represents shares of the Issuers Class A Common Stock received by the Reporting Person pursuant to a dividend reinvestment feature under the Issuer's stock plan since the last Statement of Changes in Beneficial Ownership was filed by the Reporting Person. Such acquisitions are exempt from Section 16 reporting requirements pursuant to Rule 16a-11.
Includes 52,903 shares of the Issuer's Class A Common Stock acquired by the Reporting Person pursuant to the Deferred Fee Plan for Directors, which shares shall vest 180 days after termination of the Reporting Person's service as a member of the Issuer's board of directors.
Represents a stock award for shares of the Issuer's Class A Common Stock having a value of $125,000 granted on the date of election as a director at the 2014 Annual Meeting of Shareholders (January 31, 2014). Per the Deferred Fee Plan for Directors, these shares shall vest 180 days after termination of the Reporting Person's service as a member of the Issuer's board of directors.
Includes 56,245 shares of the Issuer's Class A Common Stock acquired by the Reporting Person pursuant to the Deferred Fee Plan for Directors, which shares shall vest 180 days after termination of the Reporting Person's service as a member of the Issuer's board of directors.
/s/ R. Read Hudson by power of Attorney for Jim D. Kever
2014-02-03