The present invention relates to membranes specially developed for use in chambers for artificial circulatory assistance which may be employed primarily in cardiovascular procedures, notably to produce arterial capacitance, to regulate blood pressure, to produce aortic counterpulsation and to pump blood. The membrane circular sections of the present invention may vary in size or not depending on the function to be performed and are interconnected so that the transition between one section and the other is smooth, regardless of the size of each section. The present invention further relates to chambers and pumps for cardiopulmonary bypass and a pumping system.