PURPOSE: To provide quickly a mirror finished surface with stable accuracy by filling a vessel, which is supported by a machine frame and consists of side faces and upper and lower ends, with a grinding material, placing a cylindrical member upright within the grinding material, allowing this cylindrical member to rotate and slide along the axis, and by grinding its outside surface.

CONSTITUTION: A filled grinding material 6 is held on the rotational and sliding directions by the friction resistance of vessel 5 with side faces 2 and upper and lower end-faces 3, 4. A cylindrical member 7 placed upright within this grinding material 6 is rotated round the upright axis C as well as slided along the axis C, and now the grinding material 6 grinds the outside surface of the cylindrical member 7 in the rotational and sliding directions, to form a mirror surface. After grinding, the cylindrical member 7 is separated to outside from inside the grinding material 6 to be utilized as a core in the baking processes for ceramic tubes. This method provides mirror surface grinding of outside surfaces without unevenness, and finishing can be made quickly with stable accuracy.