PURPOSE: To obtain a spherical surface with high sphericity at all times by giving the cutting edge of a spherical surface processing machine a circular motion with the prescribed radius having its center at the intersection of the two axes so that it may machine a work to provided such a spherical surface.

CONSTITUTION: A work W, which is held by a chuck 1a of a main spindle 1, is rotated at the prescribed rotating speed. On the axis m which intersects the axis lof the main spindle 1 at the point O, a cutter shaft 2 is set to be free to rotate about this shaft m. And, when a single point tool 4 set at the tip of the shaft 2 is directed toward the intersection point O with a distance R from the tool edge to the point O, the tool edge makes a circular motion about the point O with the radius R if the shaft 2 is rotated. Therefore, if the processing machine is configured to allow the setting of any angle θ of intersection between the axis land the axis m, it is possible to set any processing range for spherical surfaces, and to obtain a spherical surface with high sphericity at all times.