When producing semiconductor bodies by a process of depositing semiconductor material from a gaseous mixture on an elongated crystalline semiconductor starting filament held between two laterally fixed supports, lateral stresses in the filaments are removed by allowing substantially friction-free, lateral movement of the filament as it is heated prior to the vapor deposition. This movement is allowed by melting a coupling segment between the filament and at least one of the supports to thereby allow lateral deformation of the coupling segment as any lateral stress of the filament is relieved. When this method is coupled with conventional means of relieving longitudinal stress in the filament, perfection in grown semiconductor bodies is maintained.