A pump may comprise a body, and a member movable relative to the body substantially along an axis of the pump. A pumping chamber may be defined by at least the body and the member. The pumping chamber may comprise a peripheral wall. The pump may further comprise an elastically deformable membrane comprising a first portion and a second portion. The first portion may be axially fixed relative to the peripheral wall, as well as being in contact with an inner surface of the peripheral wall at least in the presence of overpressure in the pumping chamber, and configured to place the pumping chamber in selective communication with at least one inlet passage. The second portion may be configured to place the pumping chamber in selective communication with at least one outlet passage.