A device (100) for assembling a pneumatic booster (200) wherein a cover (203) of the booster is housed in a support (101) and a cylindrical cap (104) whose internal volume (107) is greater than a volume of a cylinder (206) of the booster, covers the cylinder placed on the cover. A gearing element (110) of the device rotates two sets of rollers (109A and 109B) about the booster and an eccentric (118) controlled by the gearing element allows an oscillating movement of the rollers against a wall of the booster. The swaging is achieved by alternately applying the rollers (109A) and (109B) and an angle of attack (114A) of the first rollers is greater than an angle of attack (114B) of the second rollers.