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

    <schemaVersion>X0305</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2012-06-07</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000949158</issuerCik>
        <issuerName>CRAY INC</issuerName>
        <issuerTradingSymbol>CRAY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001141663</rptOwnerCik>
            <rptOwnerName>NARODICK SALLY G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>901 FIFTH AVENUE,</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1000</rptOwnerStreet2>
            <rptOwnerCity>SEATTLE</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98164</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2012-06-07</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3539</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11.09</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>56435</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Restricted stock award:  1,770 shares will vest on the earlier of (i) June 7, 2013 and (ii) the date that is immediately prior to the date of the next annual meeting of shareholders (the &quot;Annual Meeting&quot;); and the remaining 1,769 shares will vest the earlier of (i) June 7, 2014 and (ii) the date that is immediately prior to the date of the annual meeting of shareholders following the Annual Meeting.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By Michael C. Piraino, Attorney-in-Fact for Sally G. Narodick</signatureName>
        <signatureDate>2012-06-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
