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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-04-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001089821</issuerCik>
        <issuerName>BLACKROCK PENNSYLVANIA STRATEGIC MUNICIPAL TRUST</issuerName>
        <issuerTradingSymbol>BPS</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001075524</rptOwnerCik>
            <rptOwnerName>FABOZZI FRANK</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>55 EAST 52ND STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10055</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>2015-04-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>5</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value>E</value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Effective as of April 13, 2015, The BlackRock Pennsylvania Strategic Municipal Trust (the &quot;Target Fund&quot;) was reorganized into BlackRock MuniYield Pennsylvania Quality Fund (the &quot;Acquiring Fund&quot;). In the Reorganization, common shareholders of the Target Fund received common shares of the Acquiring Fund having a value equal to the aggregate NAV of the Target Fund common shares surrendered as determined at the close of business on April 10, 2015, less the costs of the Reorganization. As of April 10, 2015, the Target Fund reported a NAV per share of $14.5988 and the Acquiring Fund reported a NAV per share of $16.0538. The conversion ratio for the Target Fund's common shares was 0.90936725. In the Reorganization, Frank Fabozzi received 90 common shares (and cash for fractional shares, if any) of the Acquiring Fund in exchange for his 100 common shares of the Target Fund.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Eugene Drozdetski as Attorney-in-Fact</signatureName>
        <signatureDate>2015-04-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
