A workpiece such as a semiconductor wafer is polished by pressing the workpiece against a polishing surface under a predetermined pressure. A polished surface of the workpiece is processed by pressing the workpiece against a processing surface under a predetermined pressure while the processing surface makes circulatory translational motion along a predetermined path. The processing surface comprises a surface of a polishing cloth or a surface of an abrading plate, and the polished surface of the workpiece is further polished or cleaned.