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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-06-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001645926</issuerCik>
        <issuerName>Multi Packaging Solutions International Ltd</issuerName>
        <issuerTradingSymbol>MPSX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001548624</rptOwnerCik>
            <rptOwnerName>Carlyle Group Management L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>1001 PENNSYLVANIA AVE. NW, SUITE 220S</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20004-2505</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001475444</rptOwnerCik>
            <rptOwnerName>TC Group Cayman Investment Holdings, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CAYMAN CORPORATE CENTER,</rptOwnerStreet1>
            <rptOwnerStreet2>27 HOSPITAL ROAD,</rptOwnerStreet2>
            <rptOwnerCity>GEORGE TOWN, GRAND CAYMAN</rptOwnerCity>
            <rptOwnerState>E9</rptOwnerState>
            <rptOwnerZipCode>KY1-9008</rptOwnerZipCode>
            <rptOwnerStateDescription>CAYMAN ISLANDS</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001548636</rptOwnerCik>
            <rptOwnerName>TC Group Cayman Investment Holdings Sub L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CAYMAN CORPORATE CENTER,</rptOwnerStreet1>
            <rptOwnerStreet2>27 HOSPITAL ROAD,</rptOwnerStreet2>
            <rptOwnerCity>GEORGE TOWN, GRAND CAYMAN</rptOwnerCity>
            <rptOwnerState>E9</rptOwnerState>
            <rptOwnerZipCode>KY1-9008</rptOwnerZipCode>
            <rptOwnerStateDescription>CAYMAN ISLANDS</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001527166</rptOwnerCik>
            <rptOwnerName>Carlyle Group L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>1001 PENNSYLVANIA AVE. NW, SUITE 220S</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20004</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001548629</rptOwnerCik>
            <rptOwnerName>Carlyle Holdings II GP L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>1001 PENNSYLVANIA AVE. NW, SUITE 220 S</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20004</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001548630</rptOwnerCik>
            <rptOwnerName>Carlyle Holdings II L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>1001 PENNSYLVANIA AVE. NW, SUITE 220 S</rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20004-2505</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2016-06-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5750000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>13.8475</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21163072</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">CEP III Chase S.a.r.l. is the record holder of these shares. Carlyle Group Management L.L.C. is the general partner of The Carlyle Group L.P., which is a publicly traded entity listed on NASDAQ. The Carlyle Group L.P. is the managing member of Carlyle Holdings II GP L.L.C., which is the general partner of Carlyle Holdings II L.P., which is the general partner of TC Group Cayman Investment Holdings, L.P., which is the general partner of TC Group Cayman Investment Holdings Sub L.P., which is the sole shareholder of CEP III Managing GP Holdings, Ltd., which is the general partner of CEP III Managing GP, L.P., which is the general partner of Carlyle Europe Partners III, L.P., which is the sole shareholder of CEP III Participations, S.a r.l., SICAR, which is the sole shareholder of CEP III Chase S.a.r.l.</footnote>
    </footnotes>

    <remarks>Due to the limitations of the electronic filing system, each of CEP III Managing GP Holdings, Ltd., CEP III Managing GP, L.P., Carlyle Europe Partners III, L.P., CEP III Participations S.a r.l., SICAR and CEP III Chase S.a r.l. are filing a separate Form 4.</remarks>

    <ownerSignature>
        <signatureName>Carlyle Group Management, L.L.C., By: /s/ Daniel D'Aniello, Chairman</signatureName>
        <signatureDate>2016-06-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>The Carlyle Group L.P., By: Carlyle Group Management L.L.C., its general partner, By: /s/ Daniel D'Aniello, Chairman</signatureName>
        <signatureDate>2016-06-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Carlyle Holdings II GP L.L.C., By: The Carlyle Group L.P., its managing member, By: Carlyle Group Management L.L.C., its general partner, By: /s/ Daniel D'Aniello, Chairman</signatureName>
        <signatureDate>2016-06-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Carlyle Holdings II L.P., By: /s/ Daniel D'Aniello, Chairman</signatureName>
        <signatureDate>2016-06-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>TC Group Cayman Investment Holdings, L.P., By: Carlyle Holdings II, L.P., its general partner, By: /s/ Daniel D'Aniello, Chairman</signatureName>
        <signatureDate>2016-06-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>TC Group Cayman Investment Holdings Sub L.P., By: TC Group Cayman Invesment Holdings, L.P., its general partner, By: Carlyle Holdings II, L.P., its general partner, By: /s/ Daniel D'Aniello, Chairman</signatureName>
        <signatureDate>2016-06-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
