Abstract: Method and apparatus for combined electrolytic-abrasive polishing: providing a tool electrode rotatable by means of a rotational drive and having a liquid-permeable visco-elastic polishing member attached to the surface of a conductive disk-like tool base; contacting the visco-elastic polishing member with a free curved surface of a workpiece, with the rotational axis of the tool electrode in tilted state relative to a plane averaging undulations on the free curved surface, to contact only peripheral portions of the visco-elastic polishing member retaining abrasive grains with the workpiece; supplying an electrolyte to polishing portions between the visco-elastic polishing member and workpiece; and conducting current for electrolysis across the visco-elastic polishing member and workpiece. The apparatus can perform the combined electrolytic-abrasive polishing automatically along free curved surface of a work by the use of an automatic two-dimensional feed mechanism.