<?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>0001340962</rptOwnerCik>
            <rptOwnerName>White Noel W</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>Chief Operations 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>211.0797</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>140597.4097</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>413.1283</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>11142.3828</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>2571.56</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>65.33</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>143168.9697</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 11,197.8685 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; 23,656.8132 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable SIA are achieved and the Reporting Person is employed by the Issuer on the vesting date; 12,697.226 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; and 10,978.85 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 (the Incentive Agreement) are achieved. The performance metrics are achievement of a two year (fiscal 2018-2019) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metric is not achieved, the award expires.</footnote>
        <footnote id="F5">Includes 11,197.8685 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; 23,656.8132 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable SIA are achieved and the Reporting Person is employed by Issuer on the vesting date; 12,697.226 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; 10,978.85 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; and 2,571.56 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Noel W. White</signatureName>
        <signatureDate>2017-02-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
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X0306
4
2016-12-19
0
0000100493
TYSON FOODS INC
TSN
0001340962
White Noel W
2200 W DON TYSON PARKWAY
SPRINGDALE
AR
72762
0
1
0
0
Chief Operations Officer
Class A Common Stock
2016-12-19
4
J
0
211.0797
0
A
140597.4097
D
Class A Common Stock
2017-02-09
4
J
0
413.1283
0
A
11142.3828
I
Employee Stock Purchase Plan
Class A Common Stock
2017-02-15
4
A
0
2571.56
65.33
A
143168.9697
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 11,197.8685 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; 23,656.8132 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable SIA are achieved and the Reporting Person is employed by the Issuer on the vesting date; 12,697.226 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; and 10,978.85 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 (the Incentive Agreement) are achieved. The performance metrics are achievement of a two year (fiscal 2018-2019) cumulative EBIT target as set forth in the Incentive Agreement.  If the performance metric is not achieved, the award expires.
Includes 11,197.8685 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; 23,656.8132 shares of Class A Common Stock which vest on July 1, 2018 if the performance metrics described in the applicable SIA are achieved and the Reporting Person is employed by Issuer on the vesting date; 12,697.226 shares of Class A Common Stock which vest on December 1, 2018 if the performance metrics described in the applicable SIA are achieved; 10,978.85 shares of Class A Common Stock which vest on November 18, 2019 if the performance metrics described in the applicable SIA are achieved; and 2,571.56 shares of Class A Common Stock which vest on February 14, 2020 if the performance metrics described in the applicable SIA are achieved.
/s/ Noel W. White
2017-02-17