PURPOSE: To polish a curved surface having required curvature uniformly and efficiently by forming the entire inner surface of a cylinder with approximately same curvature as that of the curved surface of a product and rotating a rotary drum through predetermined amount of polishing material.

CONSTITUTION: A spherical continuous polishing cylinder 35 is formed of metal, ceramic, synthetic resin and the like, and curved inner faces AWE are formed with same curvature as that of the curved face of a product. Predetermined amount of polishing material and an object are placed in the cylinder 35 and a cover 35a is closed, then the cylinder 35 is mounted on a plurality of cylinder receivers of a rotary drum and rotated with the axis 35C being inclined by an angle lower than 7, preferably lower than 4, with respect to the rotary shaft of the rotary drum. Consequently, the object to be polished slides while pressure contacting from the curved face A to B then to C,...E through a micro and uniform polishing material layer and reciprocates between the opposite end sections thus performing polish work. By such arrangement, a curved surface having predetermined curvature can be polished uniformly.