Abstract: A method and apparatus for machining the surface of a spherical segment, the surface being either convex or concave, by a circular milling cutter mounted on a milling machine and rotatably driven about an axis of rotation. The segment is carried by a fixture journally mounted for pivoting about a pivot axis passing through the spherical center of the surface to be cut, and the axis of rotation also passes through the spherical center. The teeth of the cutter lie in a plane perpendicular to the axis of rotation which is the furthest such plane that intersects the face of the cutter so that only the cutting teeth will contact the spherical surface to be formed. The fixture is pivoted about the pivot axis and the segment moves through and is cut by the rotating teeth to form the spherical surface.