A medical device for treating a heart valve insufficiency, with an endoprosthesis which can be introduced into a patient's body and expanded to secure a heart valve prosthesis in the patient's aorta. In an embodiment, the endoprosthesis has a plurality of positioning arches configured to be positioned with respect to a patient's aorta and a plurality of retaining arches to support a heart valve prosthesis. The endoprosthesis includes a first collapsed mode during the process of introducing it into the patient's body and a second expanded mode when it is implanted.