A forging apparatus carries out a method of manufacturing a gear having external teeth on an outer circumferential wall surface thereof and internal teeth on an inner circumferential wall surface thereof. First, an internal tooth forming die is inserted through a through hole defined in a workpiece. Next, a pressing die is caused to abut against the workpiece, and an external tooth machining die finishes the external teeth while preventing a support die from being lowered under action of damping mechanisms. Thereafter, a pressing die presses the workpiece to apply a load in excess of a preset load for the damping mechanisms. The support die is then lowered to lower the workpiece along the internal tooth forming die. At this time, the internal teeth are formed on the inner circumferential wall surface of the workpiece.