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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-01-26</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001067701</issuerCik>
        <issuerName>UNITED RENTALS INC /DE</issuerName>
        <issuerTradingSymbol>URI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001265485</rptOwnerCik>
            <rptOwnerName>KNEELAND MICHAEL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O UNITED RENTALS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>100 FIRST STAMFORD PLACE, SUITE 700</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06902</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-26</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>30000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>182.7524</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>279073</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-01-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1079</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>277994</value>
                    <footnoteId id="F4"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This transaction was made pursuant to a Rule 10b5-1 trading plan on behalf of the reporting person.</footnote>
        <footnote id="F2">Represents weighted average sale price for executed sale transactions on January 26, 2018. The range of prices for such transactions was from $180.45 to $185.18.  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 within the range.</footnote>
        <footnote id="F3">Represents a gift of shares by the reporting person to a family member.  The reporting person disclaims beneficial ownership of such transferred shares.</footnote>
        <footnote id="F4">Following this transaction, reporting person retains a substantial ownership position in Company securities and his ownership currently satisfies the Company's stock ownership guidelines.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Alison M. Walsh, Attorney-in-fact</signatureName>
        <signatureDate>2018-01-29</signatureDate>
    </ownerSignature>
</ownershipDocument>
