Abstract: A textile material is molded by preheating to its transition temperature and then rapidly deformed by stretching without cooling. The deformation is maintained for a certain time at the preheating temperature or higher. The material is then quickly cooled. An apparatus for molding particularly fabric has a heat chamber having an opening over which the fabric is fastened, and a molding body having the desired shape and movable towards the heat chamber so as to stretch the fabric while entering partly through the opening. The molding body and heat chamber can be heated and the heat chamber may be evacuated or supplied with air under pressure for cooling the fabric.