Disclosed are a method, apparatus and tool for the manufacture of a deep-bed wheel rim from a hollow cylindrical preform. In the method the metal preform is shaped to the deep-bed rim in a single mounting on a single tool of several parts, and the constriction of the middle part of the preform to make the bed is performed with concentric rotation of tool and preform. The side portions of the preform are widened to make the bead flanges by a radial shifting of the axis of rotation of the preform together with a tool part shifting appropriately in the plane perpendicular to the axis of rotation to make the bed and the bead seat. The pressing at least during the widening takes place inwardly in a single radial direction, the direction of the axial shift corresponding to the pressing direction. The invention furthermore relates to an apparatus for the practice of the method. According to the invention, this apparatus is a pressing machine with two spindles which bear a tool in common. This tool has a part which is displaceable in a plane perpendicular to the spindles' axis of rotation.