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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-06-06</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001624771</rptOwnerCik>
            <rptOwnerName>CEP III Managing GP Holdings, Ltd.</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>0001624770</rptOwnerCik>
            <rptOwnerName>CEP III Managing GP, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>50 LOTHIAN RD., FESTIVAL SQUARE</rptOwnerStreet2>
            <rptOwnerCity>EDINBURGH</rptOwnerCity>
            <rptOwnerState></rptOwnerState>
            <rptOwnerZipCode>X0 EH3 9WJ</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001624768</rptOwnerCik>
            <rptOwnerName>CEP III Participations, S.a.r.l. SICAR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>2, AVENUE CHARLES DE GAULLE, 4TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-1653</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001653975</rptOwnerCik>
            <rptOwnerName>CEP III Chase S.a.r.l.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE CARLYLE GROUP</rptOwnerStreet1>
            <rptOwnerStreet2>2, AVENUE CHARLES DE GAULLE, 4TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>LUXEMBOURG</rptOwnerCity>
            <rptOwnerState>N4</rptOwnerState>
            <rptOwnerZipCode>L-1653</rptOwnerZipCode>
            <rptOwnerStateDescription>LUXEMBOURG</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001624769</rptOwnerCik>
            <rptOwnerName>Carlyle Europe Partners III, 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>2017-06-06</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>21163072</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Disposed of in exchange for $18.00 per share pursuant to the Agreement and Plan of Merger, dated as of January 23, 2017, by and among the Issuer, WestRock Company and WRK Merger Sub Limited (&quot;Merger Sub&quot;), pursuant to which Merger Sub was merged with and into the Issuer, with the Issuer surviving such merger.</footnote>
        <footnote id="F2">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 Carlyle Group Management L.L.C., The Carlyle Group L.P., Carlyle Holdings II GP L.L.C., Carlyle Holdings II L.P., T.C. Group Cayman Investment Holdings, L.P. and T.C. Group Cayman Investment Holdings Sub L.P. are filing a separate Form 4.</remarks>

    <ownerSignature>
        <signatureName>CEP III Managing GP Holdings, Ltd., By: /s/ William Conway, Director</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CEP III Managing GP, L.P., By: William Conway, for and on behalf of CEP III Managing GP Holdings, Ltd. as general partner of CEP III Managing GP, L.P., By: /s/ William Conway</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Carlyle Europe Partners III, L.P., By: William Conway, for and on behalf of CEP III Managing GP Holdings, Ltd., as general partner of CEP III Managing GP, L.P., as GP of Carlyle Europe Partners III, L.P.,
By: /s/ William Conway</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CEP III Participations, S.a r.l. SICAR, Represented by David Garcelan, as Manager and authorized representative of CEP III Managing GP Holdings, Ltd., Manager By: /s/ David Garcelon</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CEP III Chase S.a r.l. Represented by Represented by David Garcelan, as Manager and authorized representative of CEP III Managing S.a r.l., Manager By: /s/ David Garcelan</signatureName>
        <signatureDate>2017-06-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
