Abstract: An internal or external annular surface of a ring which by cold-rolling is to be profiled with accompanying tangential expansion and substantial diametrical enlargement of the ring is preliminarily profiled by a metal-shaping process other than cold-rolling, the preliminary profile having distinctly defined lateral peripheral edges spaced from the lateral walls of the workpiece. The cold-rolling is effected by a cold rolling tool having formed on the working surface thereof facing the preliminarily profiled workpiece surface a profile which is shaped to make local contact with each of the edges of the preliminary profile of the ring and thereby begin compressively stressing the ring by the local contact before the cold rolling conforms the profile of the workpiece to the profile of the tool sufficiently to substantially increase the contact of the tool profile with the workpiece profile.