The relation between flaw density and strength of ceramic or brittle materials were derived and applied to a commonly used testing method of four-point bending for determining the strengths of ceramic or brittle materials. Previous analysis failed to include the failures outside or at the inner loading positions for four-point test data. The present approach elevates such a constrain so that the relation applies to failures occurs at any points between the outer loading positions for four-point test data. (C) 2003 Kluwer Academic Publishers.