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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-06-19</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001552992</rptOwnerCik>
            <rptOwnerName>Hayes Thomas P</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>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-06-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>851.037</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>104446.0833</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>2018-07-01</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>20202</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>68.85</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>84244.0833</value>
                    <footnoteId id="F4"/>
                </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 48,388.5647 shares of Class A Common Stock which vested as described in footnote 3; 8,738.371.748 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; 20,892.614 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 17,846.547 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved.</footnote>
        <footnote id="F3">On July 1, 2018, 48,388.5647 shares of restricted Class A Common Stock vested. These shares were previously reported as beneficially owned by the Reporting Person. Pursuant to an election made by the Reporting Person, 20,202 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations.</footnote>
        <footnote id="F4">Includes 8,738.371 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; 20,892.614 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 17,846.547 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Brett Worlow by Power of Attorney for Thomas P. Hayes</signatureName>
        <signatureDate>2018-07-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2018-06-19
0
0000100493
TYSON FOODS INC
TSN
0001552992
Hayes Thomas P
2200 W. DON TYSON PARKWAY
SPRINGDALE
AR
72762
1
1
0
0
President and CEO
Class A Common Stock
2018-06-19
4
J
0
851.037
0
A
104446.0833
D
Class A Common Stock
2018-07-01
4
S
0
20202
68.85
D
84244.0833
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 48,388.5647 shares of Class A Common Stock which vested as described in footnote 3; 8,738.371.748 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; 20,892.614 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 17,846.547 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved.
On July 1, 2018, 48,388.5647 shares of restricted Class A Common Stock vested. These shares were previously reported as beneficially owned by the Reporting Person. Pursuant to an election made by the Reporting Person, 20,202 shares were sold by the Reporting Person to the Issuer to satisfy tax withholding obligations.
Includes 8,738.371 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; 20,892.614 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable Stock Incentive Agreement are achieved; and 17,846.547 shares of Class A Common Stock which vest on November 13, 2020 if the performance metrics described in the applicable Stock Incentive Agreement are achieved.
/s/ Brett Worlow by Power of Attorney for Thomas P. Hayes
2018-07-05