A pumping system comprising a membrane pump (1) for pumping a medium into or out of a vessel (6), the membrane pump comprising an actuating member (13) for moving a membrane (3) in a first direction from a first end position to a second end position against the action of a spring (12), the membrane being movable in the opposite direction from the second end position to the first end position under the action of the spring. The pumping system comprises sensing means (14) for generating a measuring value representing the location of said first end position of the membrane (3), and processing means (17) for establishing a pressure value representing the pressure inside a vessel (6) connected to an inlet (5) or outlet (24) of a pump chamber (4), the processing means (17) being adapted to establish said pressure value based on said measuring value.