The invention relates to a process and a pump for blood circulation in a human or animal body, for providing a supplementary blood supply to certain organs suffering from insufficiency or needing a blood supplement. According to the invention, the process consists in introducing a blood pump under the patients skin, in the abdominal-thoracic area, where the oxygenated blood taken from the pulmonary vein is brought by means of a tube and pushed by the pump through a delivery tube towards the organ suffering venous insufficiency, the pump being driven by the abdominal muscles, in the breath-in phase, when the perimeter of the area in which the pump is placed is in dimensional increase, keeping the pump in a fixed position, during the pumping phase, by a shield-cuirass, of a shape adapted to the area in which it is placed, and kept in operating position by some adjustable straps, crossed over the patients back, in the breath-out phase of the respiratory cycle, a spring and a pneumatic cushion accomplishing the pump blood-filling phase, the same system of shield-cuirass with fastening straps being used for the preliminary adjustment and the calibration, specific to each person, of the blood pump technical parameters, but with the pump placed on the skin under the shield-cuirass, for simulating the operation with water or other liquid, before placing the pump under the skin. As claimed by the invention, the pump consists of a first chamber (1) with elastic walls, provided with some one-way valves (8 and 9) with a connection for blood inlet and outlet and a second chamber (2) provided with other one-way valves (10 and 11) with a connection for blood inlet and outlet, the actuation of the two chambers (1 and 2) being performed by means of a rigid membrane placed between the two pumping chambers (1 and 2), membrane which is part of an actuating casing (4), comprising, in its turn, two rigid membranes connected to one another by some connecting bridges (12).Invenţia se refer