<?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>0001557040</rptOwnerCik>
            <rptOwnerName>Calaway Curt</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>SVP Controller &amp; CAO</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>266.667</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18974.109</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>2017-11-16</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>757.7534</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3429.8363</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="F4"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>961.908</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>19936.017</value>
                    <footnoteId id="F5"/>
                </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="F6"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>4115</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>4115.0</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>4115</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>2017-11-21</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3847.634</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>3847.634</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3847.634</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 1,532.726 shares of Class A Common Stock which vest on November 30, 2018 and 1,307.152 shares of Class A Common Stock which vest on November 18, 2019.</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 17, 2020.</footnote>
        <footnote id="F5">Includes 1,532.726 shares of Class A Common Stock which vest on November 30, 2018; 1,307.152 shares of Class A Common Stock which vest on November 28, 2019; and 961.908 shares of Class A Common Stock which vest on November 17, 2020.</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 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/ R. Read Hudson by Power of Attorney for Curt Calaway</signatureName>
        <signatureDate>2017-11-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2017-09-19
0
0000100493
TYSON FOODS INC
TSN
0001557040
Calaway Curt
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
SVP Controller & CAO
Class A Common Stock
2017-09-19
4
J
0
266.667
0
A
18974.109
D
Class A Common Stock
2017-11-16
4
J
0
757.7534
0
A
3429.8363
I
Employee Stock Purchase Plan
Class A Common Stock
2017-11-17
4
A
0
961.908
0
A
19936.017
D
Non-Qualified Stock Options (Right to Buy)
77.97
2017-11-17
4
A
0
4115
77.97
A
2018-11-17
2027-11-17
Class A Common Stock
4115.0
4115
D
Performance Shares
2017-11-21
4
A
0
3847.634
A
Class A Common Stock
3847.634
3847.634
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 1,532.726 shares of Class A Common Stock which vest on November 30, 2018 and 1,307.152 shares of Class A Common Stock which vest on November 18, 2019.
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 17, 2020.
Includes 1,532.726 shares of Class A Common Stock which vest on November 30, 2018; 1,307.152 shares of Class A Common Stock which vest on November 28, 2019; and 961.908 shares of Class A Common Stock which vest on November 17, 2020.
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/ R. Read Hudson by Power of Attorney for Curt Calaway
2017-11-21