LIMITED POWER OF ATTORNEY

	The undersigned hereby constitutes and appoints Andrew Gengos and David Gaiero,
and each of them individually, with full power of substitution, as the
undersigned's true and lawful attorney-in-fact to:

(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.

	The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that each such attorney-in-fact, or each
such attorney-in-fact's substitute or substitutes, shall lawfully do or cause to
be done by virtue of this power of attorney and the rights and powers herein
granted.  The undersigned acknowledges that each foregoing attorney-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934, as amended.

	This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, 5, and any Schedules 13D
or 13G with respect to the undersigned's holdings of and transactions in
securities issued by the Company, unless earlier revoked by the undersigned in a
signed writing delivered to each foregoing attorney-in-fact.

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	IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 2nd day of May, 2022.


		/s/ Adam Veness
		---------------------------
		Name: Adam Veness