PURPOSE: To prevent streaks from occurring in the traces even if nonfeeding polishing is performed, by having a relative position between a rotary elastic body and a workpiece reciprocatively displaced in the same direction with a turning axis of the rotary elastic body in succession, during rotation of the rotary elastic body.

CONSTITUTION: A Y table 12 is being stopped as rotating a rotary elastic body 5, and an X table 10 is reciprocatively displaced at a fine stroke as if it is vibrated. With this constitution, a polished part 8a of a workpiece 8 is polished at a minute vertical strip area G1 conformed to a displacement stroke of the X table 10. In consequence, occurrence of streak flaw is prevented in the polishing traces despite nonfeeding polishing.