Device for shaping a, preferably tubular, hollow body which has a hollow body wall, a hollow body interior delimited by the hollow body wall, and a hollow body axis which extends perpendicularly to a hollow body cross section, • comprising a shaping die which has a die opening and a shaping means provided on the die opening, • comprising an axial hollow body abutment, • comprising a feed drive, by means of which the shaping die and the axial hollow body abutment can be moved toward one another with an axial shaping movement, wherein, during a shaping process, the shaping die is sitting on the hollow body that is to be shaped and, on the outer face of the hollow body, engages in the hollow body wall by means of the shaping means, and wherein, during the shaping process, the shaping die and the axial hollow body abutment being movable toward one another along the hollow body axis with the axial shaping movement to shape the hollow body, and wherein, during the shaping process, the axial hollow body abutment being pressurized in the axial direction by the hollow body due to pressurization which takes place at a pressurization point of the hollow body by means of the shaping means of the shaping die that engages in the hollow body wall, and the hollow body being supported by the axial hollow body abutment in the opposite direction to the axial pressurization of the axial hollow body abutment, and • comprising an inner support body which is associated with the hollow body interior, which support body is arranged in the hollow body interior during the shaping process and supports the hollow body wall in the radial direction of the hollow body axis, and which also forms an axial auxiliary abutment, on the support body side, for the hollow body, • the axial auxiliary abutment for the hollow body, which is on the support body side, being arranged during the shaping process on the side of the pressurization point of the hollow body that is remote from the axial hollow body abutment along the hollow body axis, and supporting the hollow body in the opposite direction to the axial pressurization of the axial hollow body abutment while the hollow body is simultaneously supported by the axial hollow body abutment, characterized in that a control device is provided for the axial hollow body abutment, by means of which a yieldingness of the axial hollow body abutment in the direction of the axial pressurization of the axial hollow body abutment can be controlled depending on the amount of axial pressurization of the axial hollow body abutment. • comprising a shaping die which has a die opening and a shaping means provided on the die opening, • comprising an axial hollow body abutment, • comprising a feed drive, by means of which the shaping die and the axial hollow body abutment can be moved toward one another with an axial shaping movement, wherein, during a shaping process, the shaping die is sitting on the hollow body that is to be shaped and, on the outer face of the hollow body, engages in the hollow body wall by means of the shaping means, and wherein, during the shaping process, the shaping die and the axial hollow body abutment being movable toward one another along the hollow body axis with the axial shaping movement to shape the hollow body, and wherein, during the shaping process, the axial hollow body abutment being pressurized in the axial direction by the hollow body due to pressurization which takes place at a pressurization point of the hollow body by means of the shaping means of the shaping die that engages in the hollow body wall, and the hollow body being supported by the axial hollow body abutment in the opposite direction to the axial pressurization of the axial hollow body abutment, and • comprising an inner support body which is associated with the hollow body interior, which support body is arranged in the hollow body interior during the shaping process and supports the hollow body wall in the radial direction of the hollow body axis, and which also forms an axial auxiliary abutment, on the support body side, for the hollow body, • the axial auxiliary abutment for the hollow body, which is on the support body side, being arranged during the shaping process on the side of the pressurization point of the hollow body that is remote from the axial hollow body abutment along the hollow body axis, and supporting the hollow body in the opposite direction to the axial pressurization of the axial hollow body abutment while the hollow body is simultaneously supported by the axial hollow body abutment,