Abstract: The arrangement for abrasive machining comprises a base member, connected with the headstock of a copy milling machine, and a casing, made in the form of a hollow cylinder, connected with the base member by articulated suspensions. Mounted in the seat of the hollow cylinder, by means of an intermediate sleeve, is a tool spindle which carries the abrasive tool. The intermediate sleeve has a spherical bearing with a flat end. The tool spindle is coupled to the rotary drive means by a flexible shaft and an intermediate shaft joined together by a splined joint. The arrangement also comprises a device for urging the abrasive tool against the surface to be machined, which includes an urging force adjustment means formed by a socket disposed in the hollow cylinder, spring-biased towards the flat end of the spherical bearing by its end and provided with a central hole for receiving the flexible shaft.