PURPOSE: To polish the form of a convex-spherical surface in an accurate manner as well as to improve its machining capacity ever so better, by supplying the inner wall of a cylindrical body with free abrasive grains, while constituting them so as to make a main flat surface on a workpiece machinable so well, in case of polishing operation for a disc type crystal vibrator or the like.

CONSTITUTION: A circular crystal plate 200 or a workpiece is secured tight to each of work locking plates 11 and 12 connected to a work holding part 8 and each of gears 9 and 10 by means of a bonding agent 24. The crystal plate 200 is machined as being pushed to free abrasive grains fed to the inner wall of a cylindrical body 100 by rotary motion in the cylindrical body 100 and reciprocating motion in the holding part 8 as well as each rotary motion in these locking plates 11 and 12, thus such a circular crystal plate as being of curved surface on one side as machined to the same curved surface (R surface) as an inner wall radius R of the cylindrical body 100. With this constitution, not only the form of a convex-spherical surface is accurately polished but also machining capacity is improvable ever so high.