The invention concerns a process and an apparatus for producing hollow bodies of thermoplastic material by means of extrusion blow molding. A tubular preform of plasticised material is expanded beyond parts of a blow molding mold enclosing it, by means of increased external pressure, wherein the preform, prior to closure of the mold halves, is spread transversely with respect to the extrusion direction and in a separation plane of the blow molding mold, in such a way that it extends between the lateral edges of the mold cavity of the blow molding mold. Prior to removal of the article from the blow molding mold, the bulge portion produced after closure of the blow molding mold is cut open along its length at each of the two sides of the mold at the respective edges extending in the extrusion direction.