Disclosed is a method of manufacturing a catalytic converter for purifying exhaust gases from an internal combustion engine wherein the converter exhibits a monolithic ceramic substrate surrounded by a supporting mat. The method includes the steps of: wrapping the substrate in a sufficient amount of supporting mat material and inserting the wrapped substrate into the metal shell; forming a cylindrical metal shell having an inner surface exhibiting substantially the same curvature as the wrapped substrate; compressively closing the metal shell around the wrapped substrate to an optimized mat density range thereby resulting in the supporting mat exhibiting a substantially uniform and maximum safe compressive stress on the substrate; and, securing together metal shell to provide a gas tight seal and to hold the compressive stress. The optimized mat density range determined by plotting the mat density-mat holding pressure relationship and the mat density-retained cyclic strength ratio relationship of the supporting mat material on a common graph and selecting an optimized range on the mat density-mat holding pressure, and thereafter obtaining the corresponding optimized mat density range.