PURPOSE: To improve polishing power, uniform polishing, surface finish and polishing speed and thereby prevent the evolution of minute cracks on the surface of an object to be polished or a ceramic molding by using a silicon carbide or silicon nitride sinter.

CONSTITUTION: A composition comprising 85 wt.% silicon carbide or silicon nitride powder (A) having a purity of 90% or more, with a sintering aid, a binder for molding and, if necessary, a dispersant, antifoaming agent, lubricant, etc., is molded, degreased and thereafter sintered in a vacuum of 5 × 10-2 - 10-5 Torr or in an inert atmosphere to obtain the title medium comprising a sinter of the powder A.