A machine for grinding a cylindrical surface and the end surface of a shoulder portion, both formed on a workpiece, using an angular grinding wheel. The end surface is perpendicular to the cylindrical surface. The grinding wheel has a first outer surface parallel to the axis of the workpiece and a second outer surface perpendicular to the first outer surface. The first outer surface has a cylinder-grinding parallel surface and a cylinder-grinding tilted surface. The parallel surface has a generatrix parallel to the generatrix of the cylindrical surface to be ground. The tilted surface is continuous with the parallel surface and has a generatrix tilted away from the generatrix of the cylindrical surface. The second outer surface has a shoulder-grinding parallel surface and a shoulder-grinding tilted surface continuous with this parallel surface. The shoulder-grinding parallel surface has a generatrix parallel to the end surface of the shoulder portion. The shoulder-grinding tilted surface has a generatrix tilted away from the end surface of the shoulder portion. The grinding wheel is fed into the shoulder portion from a given position located radially inside the end surface. Then, the wheel is moved radially outwardly to grind the end surface. Subsequently, the wheel is moved relative to the workpiece along the generatrix of the cylindrical surface away from the end surface to grind the cylindrical surface.