An indirect extrusion press including a press frame body of the Rahmen structure. The press frame body is formed of a press platen and a main cylinder frame, which are rigidly connected together. Movably disposed between the press platen and main cylinder frame is a container adapted to retain a billet therein. A die stem fixedly extends toward the container from the platen while a pressing stem slidably extends toward the container from the main cylinder frame. Hydraulic cylinders are provided with the platen to shift the container back and forth along the longitudinal center line of the press. Hydraulic coupling cylinders are also provided with a crosshead from which the pressing stem extends and the pistons of both cylinders are connected to their respective container holders. The relative position of the container and pressing stem is maintained constant during an extrusion stroke so that the container-shifting force is added to an extrusion force. An effective scalping operation of the container is performed by using not only the container-shifting cylinders but also the coupling cylinders. An intermediate frame may also be slidably provided on the die stem such that the shifting force for the intermediate frame may also be added to the extrusion force or scalping force. The extra extrusion force is received by the container and its related moving members, thereby enabling use of the press frame body without reinforcement and allowing a reduction in the total number of parts and weight necessary, and simplification of the press.