Abstract: A casing for a vibration damper of a motor-vehicle comprises a container tube and a side tube with the side tube axis being substantially transverse to the container tube axis. The side tube is shaped such as to accommodate a bypass valve the opening and closing of which effects a variation of the damping behaviour of the vibration damper. The side tube is made from a side tube preproduct which has a bottom wall and a contact face adapted to the radially outer circumferential surface of the container tube. The side tube is positioned on the radially outer circumferential surface of the container tube by positioning the contact face onto the radially outer circumferential surface of the container tube. Hereupon, the side tube is fastened by welding to the container tube along the circumference of the contact face. Hereupon, a connection passage is made between a cavity of the side tube and a cavity of the container tube.