Abstract: A continuous caster mold has a water-cooled inner wall of copper or a copper alloy that is thoroughly covered with pieces of ceramics. A continuous casting process, which uses a mold whose inner wall of copper or a copper alloy is lined with ceramics having resistance to wear, heat and thermal shock, heat conductivity and lubricating property, with the thickness of the ceramics lining varied either stepwise or continuously in the casting direction. The molten metal, which progressively solidifies as its heat is extracted, is withdrawn by taking advantage of the solid lubrication provided by the ceramics lining. The thickness of the lining is varied to prevent the formation of air gaps between the surface of the lining and the solidifying shell and cool the steel being cast according to the desired pattern, and/or to start solidification of the molten metal below the molten metal surface level.