To completely prevent burrs generated in an outwardly expanding manner toward both ends of a stepped groove during the pressing operation by machining a surface passing a part forming an end face of the groove after the forming is completed and extending in the axial direction in advance on an outer circumference of a round bar stock before pressed by a stepped groove forming device.

Two faces 1a and 1b are formed on an outer circumferential surface of a round bar stock M in the axial direction through the cold drawing to form a two-faced round bar M1. The two-faced round bar M1 is folded in U-shape and machined into a U-shaped frame. Leg parts of the U-shaped frame are pressed to form a stepped groove 3 on an outer circumferential surface on the surface 1a side and the surface 1b side by a round bar stepped groove forming device. When the excessive material to form the outer circumferential surface of the U-shaped frame to be pressed is deformed outwardly, both ends of the stepped groove 3 are expanded outwardly to prevent generation of burrs. This method is useful in forming the stepped groove 3 in the round bar M of an electro-resistance welded tube used for a head rest for automobile applications.