SUBSTITUTE POWER OF ATTORNEY

	Pursuant to the Limited Power of Attorney of John Thero (the "Power of
Attorney"), dated February 4, 2022 and filed with the Securities and Exchange
Commission, the undersigned has been constituted and appointed true and lawful
attorney-in-fact, with full power of substitution, to, on behalf of Mr. Thero:

(1)	prepare, execute in the undersigned's name and on the undersigned's behalf,
and submit to the U.S. Securities and Exchange Commission (the "SEC") a Form ID,
including amendments thereto, and any other documents necessary or appropriate
to obtain codes and passwords enabling the undersigned to make electronic
filings with the SEC of reports required by Section 16(a) of the Securities
Exchange Act of 1934, as amended, or any rule or regulation of the SEC;

(2)	execute for and on behalf of the undersigned, in the undersigned's capacity
as officer and/or director of Cyteir Therapeutics, Inc. (the "Company"), Forms
3, 4, 5 and any Schedules 13D or 13G in accordance with Section 16(a) of the
Securities Exchange Act of 1934, as amended, and the rules thereunder;

(3)		do and perform any and all acts for and on behalf of the undersigned that
may be necessary or desirable to complete and execute any such Form 3, 4, or 5
or Schedule 13D or 13G, complete and execute any amendment or amendments
thereto, and timely file such form with the SEC and any stock exchange or
similar authority; and

(4)	take any other action of any type whatsoever in connection with the
foregoing that, in the opinion of each such attorney-in-fact, may be of benefit
to, in the best interest of, or legally required by, the undersigned, it being
understood that the documents executed by each such attorney-in-fact on behalf
of the undersigned pursuant to this Power of Attorney shall be in such form and
shall contain such terms and conditions as each such attorney-in-fact may
approve in each such attorney-in-fact's discretion.

	Pursuant to the powers granted to the undersigned in the Power of Attorney, the
undersigned hereby constitutes and appoints Adam Veness as a substitute to the
undersigned attorney-in-fact, with full power of substitution, and with full
power and authority to do and perform every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of the rights and powers granted
to the undersigned in said Power of Attorney.  For the avoidance of doubt, the
foregoing appointment shall not serve as a revocation of the powers granted to
the undersigned himself in the Power of Attorney.

	This Substitute Power of Attorney shall remain in full force and effect unless
and until revoked by the undersigned.

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	IN WITNESS WHEREOF, the undersigned has caused this Substitute Power of
Attorney to be executed as of this 12th day of May, 2022.


		/s/ David Gaireo
		-------------------
		David Gaiero