A ribbing process, particularly for providing leather coverings, includes the steps of applying a covering material on a template that includes longitudinally extended seats, inserting longitudinally extended forming rods in the seats of the template, and making the covering material adhere to the template and providing seats in the covering material. The ribbing process also includes hot pressing a first assembly that includes the template, the covering material, and the forming rods, thermoforming the covering material, and removing the forming rods from the first assembly.