In a method for thickening a plastically deformable hollow body wall of a hollow body, with effective radial support of the unthickened hollow body wall on an outer supporting face of an outer mold and with effective radial support of the hollow body wall on an inner supporting face of an inner supporting body, the hollow body is acted on by a compressive force by two application members at application points by moving the application members towards one another in the axial direction with a compressing movement. The application points on the hollow body are distanced from one another in the axial direction. An expansion space of the outer mold is arranged between the application points. Due to the compressing movement of the application members, material of the hollow body wall between the application points is plasticised in the region of the expansion space of the outer mold, and plasticised material of the hollow body wall flows into the expansion space of the outer mold, thus thickening the hollow body wall.