A graft or prosthetic element suitable, e.g., for replacing a tendon or ligament is fastened in a bone tunnel or blind opening with the aid of a fastener. In a first step, the graft or prosthetic element is press-fitted in the tunnel or opening by forcing the fastener into the opening or by positioning the fastener in the opening and then expanding it, wherein the fastener is in contact with the graft or prosthetic element and with the bone wall of the tunnel or blind opening. In a second step, the fastener is anchored in the bone wall of the tunnel or blind opening with the aid of a liquefiable material which is liquefied in the vicinity of the bone wall where it is in contact with the fastener and by making the liquefied material penetrate into the bone wall.