PURPOSE: To accurately bore a lens fasening hole in the direction crossing a refractive surface at a right angle.

CONSTITUTION: In a lens lapping machine equipped with a lens grinding rubstone 5 and a carriage 15 holding a rimless lens L in a manner rotatable around a lens rotary shaft, a hole position input device inputting the position of the lens fastening hole bored in the rimless lens L, a movable boring device 50 changed in its cutting direction and cutting the rimless lens L to bore the lens fastening hole, an angle-of-inclination measuring device measuring the angle of inclination of the refractive surface of the rimless lens at the position of the lens fastening hole and a control device controlling the position and direction of the boring device 50 on the basis of the position of the lens fastening hole and the angle of inclination measured by the angle-of-inclination measuring device to bore the lens fastening hole at the aforementioned position in the direction crossing the refractive surface of the rimless lens L are provided.