5 n7 A grinding machine having an angular type grinding wheel and a dressing apparatus therefor. The grinding wheel is formed with first and second grinding surfaces usable for grinding a cylindrical surface and shoulder end surface of a workpiece, respectively, and first and second reference surfaces parallel to the first and second grinding surfaces, respectively. The positions of the first and second reference surfaces and the first and second grinding surfaces are detected with touch bars before each dressing operation so as to obtain a first distance between the first grinding surface and first reference surface, and a second distance between the second grinding surface and second reference surface. After that, a first dressing amount for dressing the first grinding surface and a second dressing amount for dressing the second grinding surface are so determined that the fist distance and the second distance would have a predetermined constant relationship after dressing operation. The first grinding surface is then dressed by the first dressing amount, while the second grinding surface is dressed by the second dressing amount.