A device for treating obesity comprises a band part (1), which can be placed annularly about the stomach and includes a closure means (2, 3) for closing the gastric band after it has been placed annularly about the stomach, and an enveloping part (18) for enveloping and supporting a stomach region proximal with respect to the applied band part (1). The band part (1) and the enveloping part (18), secured in position on the band part (1) and laterally projecting from it, are implemented as a unit prefabricated by the manufacturer.