To provide an apparatus and a method for polishing, wherein the yield of a semiconductor device to be formed on the peripheral portion of a wafer is improved by uniformly flattening the whole surface of the wafer by preventing the over-polishing to be produced on the peripheral portion of the wafer.

The polishing apparatus 10 is composed of a platen 11, a platen turning means, such as a motor, a polishing pad 14 sticking to the surface of the platen, a nozzle 13 for supplying polishing fluid on the surface of the polishing pad, and a polishing head 12 which holds the wafer 15 and presses the surface of the wafer against the surface of the polishing pad. The polishing head includes a retainer ring 16 having a ring portion 16' to be arranged outside the peripheral portion of the wafer. The compressibility of the retainer ring is within 95 to 101% of that of the polishing pad, preferably within 99.4 to 100.6%.