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

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-06-17</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001662244</issuerCik>
        <issuerName>Cyteir Therapeutics, Inc.</issuerName>
        <issuerTradingSymbol>CYT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001864337</rptOwnerCik>
            <rptOwnerName>Bracken Racquel</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>128 SPRING ST, BUILDING A, SUITE 510</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>LEXINGTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02421</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Stock Option (Right to
Buy)</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>18.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <value>2031-06-17</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>17250</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">The option will vest in full on the earlier of (a) June 17, 2022 and (b) the next annual meeting of stockholders that follows June 17, 2021, in each case subject to the Reporting Person's continued service on the Issuer's board of directors through the applicable vesting date.</footnote>
        <footnote id="F2">Under an agreement between the Reporting Person and VR Management, LLC (the &quot;Management Company&quot;), the Reporting Person is deemed to hold the reported shares for the sole benefit of the Management Company and must exercise the reported shares solely upon the direction of the Management Company, which is entitled to the shares. The Management Company may be deemed the indirect beneficial owner of the reported shares, and the Reporting Person may be deemed the indirect beneficial owner of the reported shares through her interest in the Management Company. The Reporting Person disclaims beneficial ownership of the reported shares except to the extent of her pecuniary interest therein.</footnote>
    </footnotes>

    <remarks>Exhibit List: Exhibit 24 - Power of Attorney</remarks>

    <ownerSignature>
        <signatureName>By: /s/ Andrew Gengos, Attorney-in-Fact</signatureName>
        <signatureDate>2021-06-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
