An equipment for manufacturing by rolling predetermined axial-symmetric longitudinal profiles on radial surfaces (2, 3) of an annular element, comprising: - an axial-symmetrically shaped forming tool delimited by an outer radial surface having a first predetermined longitudinal profile in radial section; - first means for rotating the forming tool about a first axis and second means for exerting a lateral thrust on the forming tool perpendicular to the first axis; - an axial-symmetrically shaped mandrel revolving about a second axis parallel to the first one and arranged laterally to the forming tool, in such a position to receive the thrust exerted on the forming tool in use; a working outer radial surface of the mandrel having a second predetermined longitudinal profile in radial section; between the first profile of the tool and the second profile of the mandrel a receiving space for the annular element to be processed being delimited, the mandrel being shaped so as to thoroughly engage, in use, the annular element to be processed; - a first and a second receiving roll (14, 15) carried revolving about a third axis parallel to the first axis by a support adapted to support the perpendicular thrust exerted on the forming tool; the first and second roll (14, 15) cooperating with a first and a second radial shoulder surface (17, 18) of the mandrel between which the working surface having the second predetermined profile is delimited; and - means for idly supporting a first end of the mandrel, which first end is arranged in the direction of introduction in use of the mandrel within the annular element to be processed and which is in use intended to axially protrude from the annular element to be processed; characterized in that the first and the second radial shoulder surface (17, 18) of the mandrel have, at opposite ends (21, 22) of the second predetermined longitudinal profile, a first and a second diameter (D1, D2), respectively, differing from each other; the first diameter of the first shoulder surface being smaller than the second diameter and the first shoulder surface being arranged immediately adjacent the first end of the mandrel; and in that, in combination: i)- the second radial shoulder surface is shaped as a concave curved surface having the second diameter as maximum diameter, at opposite ends (24, 25) thereof, and which surface defines an annular groove on the mandrel, having a predetermined radial depth; and ii)- the second receiving roll has a peripherally outer edge delimited by a convex curved surface mating with the second radial concave shoulder surface and which engages the annular groove of the mandrel for keeping the mandrel axially locked and absorbing any axial thrusts generated on the mandrel. - an axial-symmetrically shaped forming tool delimited by an outer radial surface having a first predetermined longitudinal profile in radial section; - first means for rotating the forming tool about a first axis and second means for exerting a lateral thrust on the forming tool perpendicular to the first axis; - an axial-symmetrically shaped mandrel revolving about a second axis parallel to the first one and arranged laterally to the forming tool, in such a position to receive the thrust exerted on the forming tool in use; a working outer radial surface of the mandrel having a second predetermined longitudinal profile in radial section; between the first profile of the tool and the second profile of the mandrel a receiving space for the annular element to be processed being delimited, the mandrel being shaped so as to thoroughly engage, in use, the annular element to be processed; - a first and a second receiving roll (14, 15) carried revolving about a third axis parallel to the first axis by a support adapted to support the perpendicular thrust exerted on the forming tool; the first and second roll (14, 15) cooperating with a first and a second radial shoulder surface (17, 18) of the mandrel between which the working surface having the second predetermined profile is delimited; and - means for idly supporting a first end of the mandrel, which first end is arranged in the direction of introduction in use of the mandrel within the annular element to be processed and which is in use intended to axially protrude from the annular element to be processed; i)- the second radial shoulder surface is shaped as a concave curved surface having the second diameter as maximum diameter, at opposite ends (24, 25) thereof, and which surface defines an annular groove on the mandrel, having a predetermined radial depth; and ii)- the second receiving roll has a peripherally outer edge delimited by a convex curved surface mating with the second radial concave shoulder surface and which engages the annular groove of the mandrel for keeping the mandrel axially locked and absorbing any axial thrusts generated on the mandrel.