A press mold having upper and lower jaws for pressing and molding articles of ceramic material. Each jaw supports a die, at least one of which has a molding matrix. A press ring mounted around the die having the matrix. Upper and lower contoured parts made of synthetic material or rubber are respectively mounted on the upper and lower die by adhesive. Each contoured part has a matrix. One of these matrices has an inner contoured edge which corresponds to the outer edge contour of the molding made by the press mold and having an outer contoured edge at least in the areas of the smaller diameters of the molding with respect to the areas of the largest diameter of the moldings in the direction of the surface of the molding which protrudes beyond this inner contoured edge and which has an even contour, such as a circle.