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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-04-22</periodOfReport>

    <notSubjectToSection16>0</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>GEORGETOWN, 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>LUXEMBORG</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>2016-04-22</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1042499</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>26913072</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">Pro rata distribution from Chase Manco, L.P. to its limited partners.  CEP III Chase S.a r.l. is the sole shareholder of Chase Manco, G.P. Limited, which is the general partner of Chase Manco L.P.</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/ Daniel D'Aniello, Director</signatureName>
        <signatureDate>2016-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CEP III Managing GP, L.P., By: Daniel D'Aniello, for and on behalf of CEP III Managing GP Holdings, Ltd. as general partner of CEP III Managing GP, L.P., By: /s/ Daniel D'Aniello</signatureName>
        <signatureDate>2016-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Carlyle Europe Partners III, L.P., By: Daniel D'Aniello, 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/ Daniel D'Aniello</signatureName>
        <signatureDate>2016-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CEP III Participations, S.a r.l. SICAR, By: /s/ David B. Pearson, Manager</signatureName>
        <signatureDate>2016-04-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>CEP III Chase S.a r.l. Represented by Andrew Howlett-Bolton, as Manager and authorized representative of CEP III Advisor  S.a r.l., Manager,  By: /s/ Andrew Howlett-Bolton</signatureName>
        <signatureDate>2016-04-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
