An angular substrate polishing method includes the steps of holding an angular substrate having a surface to be polished within a guide ring of a substrate holding head; pressing the substrate surface to be polished, and also one surface of the guide ring, against a polishing pad; and independently rotating the polishing pad and the substrate-holding head together with the substrate it holds while pressing the polishing pad-contacting surface of the guide ring against the polishing pad, to thereby polish the substrate surface. During the polishing step, a pressing force is applied to the guide ring which is separate from the pressing force applied to the substrate, enhancing the flatness of the polished substrate.