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

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2007-01-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001289236</issuerCik>
        <issuerName>BioMed Realty Trust Inc</issuerName>
        <issuerTradingSymbol>BMR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001340833</rptOwnerCik>
            <rptOwnerName>Sztraicher Karen A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>17140 BERNARDO CENTER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 222</rptOwnerStreet2>
            <rptOwnerCity>SAN DIEGO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92128</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP - Chief Accounting Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>LTIP Units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2007-01-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>17000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>17000</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>17000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">These profits interest units of BioMed Realty, L.P. (the &quot;Operating Partnership&quot;) were granted on January 31, 2007 pursuant to the 2004 Incentive Award Plan of the Operating Partnership and BioMed Realty Trust, Inc. (the &quot;Company&quot;).  The LTIP Units are subject to time-based restrictions.</footnote>
        <footnote id="F2">LTIP Units are subject to vesting 25% on each of January 1, 2008, 2009, 2010 and 2011.  Upon the occurrence of certain &quot;triggering events,&quot; the LTIP Units can over time achieve full parity with common units of the Operating Partnership for all purposes, and therefore accrete to an economic value equivalent to one share of common stock of the Company on a one-for-one basis.  If such parity is reached, vested LTIP Units convert to common units of the Operating Partnership and then may be redeemed for cash in an amount equal to the then fair value of an equal number of shares of common stock or converted into an equal number of shares of common stock, as determined by the Company.</footnote>
        <footnote id="F3">The LTIP Units do not have an expiration date.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Gary A. Kreitzer, Attorney-in-Fact</signatureName>
        <signatureDate>2007-02-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
