A medical pump device for delivering a medical fluid includes a base body and elastomeric hollow membrane secured to the base body and arranged in such a way that a pump volume for filling with medical fluid is formed between the base body and hollow membrane. The hollow membrane, in an at least partially filled state of the pump volume, is elastically extended and exerts a delivery pressure on the pump volume. The medical pump device has a sensor system set up to determine the extension of the hollow membrane such that, by using the extension that is thus determined, filling level information concerning the filling state of the pump volume is determined. The medical pump device can be used in infusion or transfusion arrangements.
