A method produces and fills containers (1) made of thermoplastic plastic, in which an extruded plastic hose is inserted into an open mold having movable mold parts. The mold parts forming the container (1) are closed. The hose is expanded by a pressure gradient acting on the hose to form the container (1), preferably in the form of a bellows. The container is filled with filling material. The level of the filling material is raised by reducing container volume in the direction of the container opening. A container closure (5) for the container opening is formed from the hose by closing head jaws of the mold. In the region of the container closure (5), one section of the plastic hose remains unclosed to form a venting cannula (3). When the container volume is reduced, the level of the filling material is raised such that at least air is displaced from the container (1) through venting cannula (3). The venting cannula (3) is closed by closing auxiliary head jaws.