PURPOSE: To perform precision processing without making a residual-stressed layer or the like, by using fine powder of diamond to mechanically polish the surface of an Al2O3-TiC material and thereafter using a polisher to rotatively polish the surface of the material under pressure in a liquid prepared by causing fine powder of SiO2, MgO or the like to suspend in pure water.

CONSTITUTION: Fine powder, which includes at least one of SiO2, MgO, CeO2, Fe2O3, Al2O3 and TiO2 and has a grain size of 0.1μ or less, is caused to suspend by 0.5 to 20wt% in pure water. A disc-shaped polisher made of a hard cloth, Sn or the like is rotatably supported in a vessel containing the suspension. A material to be processed is placed in contact with the surface of the polisher under predetermined load in the suspension. The material and the polisher are rotated relative to each other so that the material is polished.