Known variable flow pumps (VF pumps) are characterized by significant inaccuracies in the delivery quantities. In addition, they cause cosmetic problems in the carrier after implantation as a result of their external configuration. The invention provides an implantable VF pump, which resolves the disadvantages. To achieve this, the battery-driven delivery device is configured according to piezoelectric principles and the external surface of the upper pump housing shell is provided with expansion joints.