The roll jacket making process involves producing a jacket with an external spiral raised area. The raised area is first formed running over a flat jacket cutout (9). This cutout is then wound into a cylindrical roll jacket (6), and the adjacent ream regions are connected to each other. The cutout may be rectangular, with a diagonal shaped strip (7) formed on it. This strip may be joined to the jacket cutout by perforation welding. Alternatively. the strip may be in the form of a diagonal ridge formed in the cutout by a pressing process.