A volumetric pump (1) comprising at least one first piston (20) inside a first hollow cylindrical part (23). This pump (1) has at least one inlet port (10) through which a liquid (15) can be sucked into at least one pump chamber (26) during an instroke of said piston (20), and at least one outlet port (11) through which the liquid (15) can be expelled during the outstroke of the piston (20). At least one second piston (21) is positioned opposite to the first piston (20) inside a second hollow cylindrical part (23') to create at least a second pump chamber (26') through which the liquid (15) can be sucked in through the inlet port (15) during an instroke of the second piston (21) and expelled through the outlet port (11) during the outstroke of said second piston (21). Both cylindrical parts (23, 23') are assembled end-to-end facing each other to form a housing (22). An element (24), preferably a disc, is mounted midway inside said housing (22). This element (24), which comprises the inlet and outlet ports (10, 11), is arranged to be animated by a preferably combined bidirectional linear and angular movement to cause relative to-and-fro sliding between the cylindrical housing (22) and the pistons (20, 21) along the axis of said pistons (20, 21) while closing the inlet and outlets ports (10, 11) synchronically to ensure a continuous flow delivery.