PURPOSE: To machine a spherical body with high precision sphericalness by a method wherein a work piece is rotated at low speed and at the same time a tool, the rotating axis of which makes a certain angle to the rotating axis of the work piece, is rotated at high speed.

CONSTITUTION: The work piece 1 is rotated about the rotating axis X at low speed. On the other hand, the cylindrical cutter 8 as the tool is rotated about the rotating axis C, which passes the center O of the work piece 1 and makes a certain angle to the rotating axis X, at super high speed. In this case, the ratio between the rotational frequencies of the tool 8 and of the work piece 1 is rendered to be about 1,300:1 and the rotating diameter d' of the share point 10 of the cutter 8 is rendered to be no less than the diameter D of the shperical body to be machined. When the cutter 8 is brought near to the work piece 1 under the above-mentioned condition, the abutting surface of the cutter 8 forms a compound locus of the two rotations of the cutter 8 and of the work piece 1, resulting in machining the spherical body with the center O into a body with precise sphericalness and high precision surface roughness.