Dosing pump device for medical use comprising a pumping chamber , a drive member , an annular pumping membrane , the outer edge of which is integral with the said pumping chamber and the inner edge of which is integral with a central drive part which is more rigid than the said membrane, capable of being displaced by the drive member parallel to itself between a return limit position and a displacement limit position in its expulsion stroke and vice versa in its suction stroke, these two positions being located on either side of the plane containing the outer edge of the said annular membrane, said pumping chamber comprising an inlet valve and an outlet valve opened by a depression, respectively by an overpressure in the pumping chamber, consecutive to the displacements of said annular pumping membrane, the suction stroke of said membrane resulting from the energy accumulated by the elastic deformation of the membrane during its expulsion stroke, wherein in said return limit position, said annular pumping membrane has a convex annular profile curved towards the outside of said pumping chamber, towards the drive member , so that its expulsion stroke results essentially in the energy-generating bending deformation of the suction stroke and in the annular compression/release of compression of the said convex annular profile on each outward stroke of the said membrane, the rigidity of the membrane being chosen so that the absolute pressure in the pumping chamber in the operating range of the membrane situated between the limit position of displacement and the limit position of return lies within the following range : P atm − ΔP clapet _ in + ΔP Δh _ in + ΔP c h arg e ≥ P > P νap where : P atm = atmospheric pressure P vap = vapour pressure of the pumped fluid ΔP clapet_in = pressure difference between the upstream and downstream sides of the inlet valve for its opening ΔP Ah_in = pressure difference in the upstream pipe between its distal end and the upstream side of the inlet valve due to the weight of the fluid column ΔP charge = pressure drop in the upstream pipe for the desired flow rate, the membrane being subject to prestress in its extreme return position, characterised in that the membrane has a truncated cone shape in the resting state and in that its displacement from its extreme return position to its extreme displacement position causes buckling resulting in an S-shaped pressure-displacement characteristic. P atm = atmospheric pressure P vap = vapour pressure of the pumped fluid ΔP clapet_in = pressure difference between the upstream and downstream sides of the inlet valve for its opening ΔP Ah_in = pressure difference in the upstream pipe between its distal end and the upstream side of the inlet valve due to the weight of the fluid column ΔP charge = pressure drop in the upstream pipe for the desired flow rate, the membrane being subject to prestress in its extreme return position, characterised in that the membrane has a truncated cone shape in the resting state and in that its displacement from its extreme return position to its extreme displacement position causes buckling resulting in an S-shaped pressure-displacement characteristic. <EOS>