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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-08-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000110621</issuerCik>
        <issuerName>RPM INTERNATIONAL INC/DE/</issuerName>
        <issuerTradingSymbol>RPM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001546776</rptOwnerCik>
            <rptOwnerName>Ratajczak Matthew T</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2628 PEARL ROAD</rptOwnerStreet1>
            <rptOwnerStreet2>P.O. BOX 777</rptOwnerStreet2>
            <rptOwnerCity>MEDINA</rptOwnerCity>
            <rptOwnerState>OH</rptOwnerState>
            <rptOwnerZipCode>44258</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP-Global Tax and Treasurer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, $0.01 par value</value>
            </securityTitle>
            <transactionDate>
                <value>2016-08-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>4152</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>54.0387</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>44402</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Price reported constitutes the average weighted price of shares sold.  Shares were sold at varying prices in the range of $53.9601 - $54.1.  The reporting person hereby undertakes, upon request by the Commission staff, the issuer or a security holder of the issuer, to provide full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F2">Includes an aggregate of 632 shares of Common Stock issued pursuant to the 1997 RPM International Inc. Restricted Stock Plan, as amended, 18,020 shares of Common Stock issued pursuant to the 2007 RPM International Inc. Restricted Stock Plan, 16,400 shares of Common Stock, issued as Performance Earned Restricted Stock, pursuant to the RPM International Inc. 2004 and 2014 Omnibus Equity and Incentive Plans, and 5,000 shares of Common Stock, issued as Performance Contingent Restricted Stock, pursuant to the RPM International Inc. 2014 Omnibus Equity and Incentive Plan. The reporting person's last Form 4, filed on July 27, 2016, incorrectly listed 58,454 total shares in Column 5 due to a mathematical error. The total as of such date was 48,554 shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Matthew T. Ratajczak, by Gregory J. Dziak, his attorney-in-fact pursuant to Power of Attorney dated April 4, 2012 on file with the Commission</signatureName>
        <signatureDate>2016-08-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
