PURPOSE: To carry out stable EEM polishing by attaching an elastomer ball to the lower end of a vertical rotary shaft to rotate the elastomer ball and giving a predetermined controllably variable slight force to said shaft.

CONSTITUTION: A vertical shaft 6 having the lower end attached to a polyurethane ball 7 is horizontally air slided by air slides 2, 3 in the direction Y and devised to be always subjected to any certain slight force directed to the working surface of a workpiece 9 to be polished. Here the workpiece 9 is mounted vertically on an arm 11 of a X-Z numerical control means 10. As a result, a rotary shaft is stably supported against gravity while the elastomer ball is adapted to approach the workpiece by the air slide and an extremely slight approach load can be stably controlled so that extremely stable and accurate EEM polishing can be carried out.