In a process for the casting of a mounting which is to be attached to the human body and which takes the form of a prosthesis socket or of an orthosis part, a reinforcement in the shape of a grid or frame located in the core region is surrounded by a polyurethane in such a way as to eliminate separation of the individual layers. The process is characterized by the following steps in the stated sequence: a) at the position of a PU sublayer which is below the reinforcement, a spacer material which can be saturated with the incompletely reacted polyurethane and which takes the form of the desired limb-proximal PU sublayer, b) the reinforcement in the shape of a grid or frame is produced thereon, c) the reinforcement is removed, d) the first polyurethane sublayer is cast with saturation of the spacer material, e) the reinforcement is again superposed on the polyurethane surface of the first polyurethane sublayer in a state of polymerization after achievement of dimensional stability, f) a further spacer material which can be saturated with the incompletely reacted polyurethane and takes the form of the desired further PU sublayer is applied and g) the further PU sublayer is cast with saturation of the second spacer material, so that where the two PU sublayers come into contact during hardening of the polyurethane of the superposed PU sublayer the two PU sublayers bond reactively with the aid of a primer applied between the PU sublayers and/or via a shared hardening process of the two PU sublayers and enclose the reinforcement.