A drum-type polishing apparatus for producing a flat mirror polish on an object such as a semiconductor wafer, is capable of three degrees of freedom of movement of a drum member with respect to the wafer. The relative movements can be made, successively or simultaneously, at right angles to an axis of the drum, parallel to the surface of the wafer, as well as at any desired angular orientations. Combined with a follower device to provide automatic compensation for unevenness in pressing pressure applied to the wafer during polishing, the polishing apparatus offers outstanding uniformity in polishing quality and high productivity, even for large diameter wafers, with a comparatively modest investment in both facility space and equipment cost.