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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2008-12-19</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>411 FIRST AVENUE S.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 600</rptOwnerStreet2>
            <rptOwnerCity>SEATTLE</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98104</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>2008-12-19</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>433</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>24797</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Additional restricted stock issued pursuant to the equity compensation
program for directors: 128 shares at $7.8108 per share and 305 shares at $6.5657 per share, with 64 shares unrestricted, 153 shares vesting May 8, 2009, 64 shares vesting May 20, 2009 and 152 shares vesting May 8, 2010.  Exempt from Section 16(b) pursuant to Rule 16b-3(d).</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Sally G. Narodick, by Kenneth W. Johnson, Attorney-in-Fact</signatureName>
        <signatureDate>2008-12-22</signatureDate>
    </ownerSignature>
</ownershipDocument>
