A method for fastening a rebound stop to a piston rod of a vibration damper positioned at a piston rod and axially supported with a first tool. A second tool component having a press-in surface that presses the tubular portion of the rebound stop into the circumferential groove of the piston rod. The first and the second tool carry out an movement toward one another. At least one tool presses the tubular portion of the rebound stop into the circumferential groove of the piston rod. The pitch angle of the press-in surface varies over the axial longitudinal extension of the press-in surface. As the distance between the tools decreases, the force ratio between the axially directed pressing force and the radially directed pressing force changes such that the axially directed pressing force decreases and the radially directed pressing force increases.