A ceramic porous body composed principally of silicon carbide or silicon nitride which has higher strength, higher heat resistance and higher thermal shock resistance and has a large number of fine pores, and a method of producing the same. The ceramic porous body, comprised principally of silicon carbide or silicon nitride, has a pore diameter of not more than 1 .mu.m, with a porosity of not less than 35%, and has a flexural strength of not less than 100 MPa. The ceramic porous body is produced by using a silicon oligomer which is capable of producing silicon carbide or silicon nitride when calcined, mixing the silicon oligomer with a silicon carbide powder or silicon nitride powder, and/or other ceramic powder which has a mean particle diameter of not more than 1.0 .mu.m, molding the mixture into shape, then sintering the molding in a suitable atmosphere at temperatures of not less than 1200.degree. C.