Abstract: An automatic grinding machine adapted to form a desired profile of the peripheral ridge of a spectacle lens which mates with the profile of the lens receiving groove of a spectacle frame. During the semi-finishing grinding step, the peripheral edge of the spectacle lens is ground by a semi-finishing grinding wheel whose outer cylindrical surface is formed with a V-shaped circumferential groove having a width greater than the thickness of the spectacle lens at the peripheral edge thereof, so that the axial center of the spectacle lens may be automatically aligned with that of the semi-finishing grinding wheel by the self-alignment action due to the contact of the peripheral edges of the spectacle lens with the inclined surfaces of the V-shaped groove.