PURPOSE: To machine a work which requires machining of recessed spherical surfaces, protruded spherical surfaces, recessed non-spherical surfaces, and protruded non-spherical surfaces.

CONSTITUTION: A supporting section 3 is provided on a base shaft 2 for the supporting section mounted erectedly on a foundation bed through a sliding mechanism 1b. A spindle casing 5 is provided on the supporting section 3 through an inclination mechanism 4. A base frame is installed on the spindle 6, and multiple cutters 8 are fixed. A work is fixed in a chuck mechanism 9 protruded from the foundation bed and rotated, the base frame 7 is inclined by the inclination mechanism 4 relative to the work, and the spindle 6 is rotated for machining to form protruded spherical surfaces, protruded non-spherical surfaces, recessed spherical surfaces, and recessed non-spherical surfaces. This method is an epoch-making one capable of making highly accurate machining of spherical or non-spherical surfaces and flat surfaces in unit of micron.