PURPOSE: To automatically replace a cylindrical polishing member by installing a drum onto the cylindrical polishing member positioned at the taking-out part of a feeding stocker and fitting the basic edge part of the drum into the cut part of a demounting member and shifting the edge part of the drum in the axial direction.

CONSTITUTION: A drum 1 is inserted into a cylindrical polishing member 2 positioned at the taking-out part 13 of a feeding stocker 12, leaving the basic edge part, by a robot, etc. and mounted, and then the prescribed grinding work is started. When replacement becomes necessary because of ehxaustion, the basic edge part of the drum 1 is fitted into the cut part 26 of a demounting member 21 in a recovery station 20, and then the edge surface of the cylindrical polishing member 2 is attached onto the demounting member 21 by shifting the edge part of the drum 1 to the basic edge part side in the axial direction, and then the cylindrical polishing member 2 is demounted from the drum 1. Then, the drum 1 is shifted to the taking-out part 13, and a new cylindrical polishing member 2 is installed. Thus, only the cylindrical polishing member can be replaced automatically, and the working efficiency can be improved.