A method for axially shaping a tube with the aid of a mandrel, which is guided in the tube, and an annular die, which is guided on the outside of the tube and the inside diameter of which is smaller than the original outside diameter of the tube; wherein the annular die has on its inner side at least one conical, axially extending transitional section (120-I, 120-II), wherein the mandrel has on its outer side at least one conical, axially extending transitional section (110-I, 110-II), and wherein the die and the mandrel form in their opposed position an annular gap for passing through and shaping the wall of the tube; wherein the method comprises the following steps: - clamping the tube with an original wall thickness in a clamping device such that at least one free section of the tube remains in order to shape the tube; a) inserting the mandrel into the tube; b) reducing the outside diameter of the tube by moving the annular die toward the clamping device in a pushing direction over the free section of the tube, wherein the mandrel leads the die in the pushing direction; and wherein the following steps are carried out when an end position is reached: c) reversing the direction of movement of the die and the mandrel from the pushing direction into an opposite pulling direction; d') first setting step: moving the die and the mandrel relative to one another to a first predetermined annular gap setting; and e') first shaping step: moving the die and the mandrel in the pulling direction over a first portion of the free tube section while maintaining the first predetermined annular gap setting in order to shape the tube; characterized in that the step sequence setting step and subsequent shaping step is repeated at least one more time, wherein the die and the mandrel are set to a new annular gap setting, which differs from the respectively preceding annular gap setting, in each additional setting step; and in that the die and the mandrel are in at least one of the setting steps moved relative to one another to a negative annular gap setting, in which the conical transitional sections (110-I, 120-I)of the die and the mandrel, which are tapered toward the free end of the tube, form the annular gap on the rear side of the die viewed in the pulling direction of the die and the mandrel. wherein the annular die has on its inner side at least one conical, axially extending transitional section (120-I, 120-II), wherein the mandrel has on its outer side at least one conical, axially extending transitional section (110-I, 110-II), and wherein the die and the mandrel form in their opposed position an annular gap for passing through and shaping the wall of the tube; wherein the method comprises the following steps: - clamping the tube with an original wall thickness in a clamping device such that at least one free section of the tube remains in order to shape the tube; a) inserting the mandrel into the tube; b) reducing the outside diameter of the tube by moving the annular die toward the clamping device in a pushing direction over the free section of the tube, wherein the mandrel leads the die in the pushing direction; and - clamping the tube with an original wall thickness in a clamping device such that at least one free section of the tube remains in order to shape the tube; a) inserting the mandrel into the tube; b) reducing the outside diameter of the tube by moving the annular die toward the clamping device in a pushing direction over the free section of the tube, wherein the mandrel leads the die in the pushing direction; and a) inserting the mandrel into the tube; b) reducing the outside diameter of the tube by moving the annular die toward the clamping device in a pushing direction over the free section of the tube, wherein the mandrel leads the die in the pushing direction; and wherein the following steps are carried out when an end position is reached: c) reversing the direction of movement of the die and the mandrel from the pushing direction into an opposite pulling direction; d') first setting step: moving the die and the mandrel relative to one another to a first predetermined annular gap setting; and e') first shaping step: moving the die and the mandrel in the pulling direction over a first portion of the free tube section while maintaining the first predetermined annular gap setting in order to shape the tube; c) reversing the direction of movement of the die and the mandrel from the pushing direction into an opposite pulling direction; d') first setting step: moving the die and the mandrel relative to one another to a first predetermined annular gap setting; and e') first shaping step: moving the die and the mandrel in the pulling direction over a first portion of the free tube section while maintaining the first predetermined annular gap setting in order to shape the tube; characterized in that the step sequence setting step and subsequent shaping step is repeated at least one more time, wherein the die and the mandrel are set to a new annular gap setting, which differs from the respectively preceding annular gap setting, in each additional setting step; and in that the die and the mandrel are in at least one of the setting steps moved relative to one another to a negative annular gap setting, in which the conical transitional sections (110-I, 120-I)of the die and the mandrel, which are tapered toward the free end of the tube, form the annular gap on the rear side of the die viewed in the pulling direction of the die and the mandrel.