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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2016-08-19</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000917470</issuerCik>
        <issuerName>OLYMPIC STEEL INC</issuerName>
        <issuerTradingSymbol>ZEUS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001682850</rptOwnerCik>
            <rptOwnerName>Greiff Andrew S</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O OLYMPIC STEEL, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>22901 MILLCREEK BLVD., SUITE 650</rptOwnerStreet2>
            <rptOwnerCity>HIGHLAND HILLS</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>44122</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP and COO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5521</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Share Units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>2158</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Share Units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>640</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
        <derivativeHolding>
            <securityTitle>
                <value>Restricted Share Units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F4"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F4"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>17318</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each restricted share unit (&quot;RSU&quot;) represents the contingent right to receive one share of Olympic Steel, Inc. common stock.</footnote>
        <footnote id="F2">The RSUs were acquired in connection with Olympic Steel, Inc.'s Senior Management Compensation Program, are fully vested for the Reporting Person and will be settled upon retirement, or earlier upon the executive's death or disability or upon a change in control of Olympic Steel, Inc., in each case in accordance with the applicable award agreement.</footnote>
        <footnote id="F3">These RSUs were acquired under Olympic Steel's Amended and Restated 2007 Omnibus Incentive Plan. These RSUs vest on July 1, 2021 if the Reporting Person continues to be an employee of Olympic Steel (or its subsidiaries or affiliates) in the same or a higher position on such date. Any vested RSUs will be settled within 30 days following the first to occur of the Reporting Person's death, disability or retirement after the Reporting Person has attained the age of 62. Vesting and settlement may also occur earlier in limited circumstances as specified in the award agreement.</footnote>
        <footnote id="F4">These RSUs were acquired in connection with Olympic Steel's Supplemental Executive Retirement Plan, are fully vested for the Reporting Person, and will be settled upon the earlier of age 62 or departure from the Issuer (or earlier in limited circumstances specified in the award agreement).</footnote>
    </footnotes>

    <remarks>Exhibit 24-Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>/s/ Gretchen A. Sterling, as Attorney-in-Fact</signatureName>
        <signatureDate>2016-08-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
