The production of pouch-shaped or pot-shaped parts is undertaken in two steps. In the first step, a film located above a die is pressed by a stamp into a cavity that reproduces the part and is subsequently pressed apart in the lower region of the cavity by deformation of the stamp in this region. The device has a rubber-like stamp that expands out on all sides once it has reached the bottom wall of the cavity and causes the film to conform to the shape of the cavity. The stamp is preferably designed in two parts, wherein a stamp insert is guided within a stamp guide and the stamp insert then has at least one deformable region. For removal of the formed film, provision is made that the die can be swung open.