The purpose of the present invention is to propose a new way of manufacturing curved metal tubes or rods with arbitrary sections and eliminating the conventional bending defects such as thinning and thickening in the wall of tube, distortion of the section, and wrinkling and folding on the surface by the extrusion bending process that can extrude and weld together one or more billets inside dies cavity, and can bend them during extrusion due to the gradient of extrusion velocities controlled by the eccentricity of the cavity sections between the entrance and the exit of the eccentric conical extrusion bending dies and conical plug, or by the relative size of the holes of multi-hole container, or by the relative moving velocity of multi-punches.