A mechanically operated liquid pump for medical and nutrient liquids, as well as for liquids used in biological and laboratory applications, has an integrated, self-contained pump construction comprising a housing having an expandable elastic member mounted wholly within the housing and shaped to store and dispense a liquid therefrom. Inlet and outlet members are also mounted within the housing, are operably connected with the elastic member inside the housing, and regulate the flow of liquid traveling into and out of the pump. A flow regulator is also mounted wholly within the housing, communicates with at least one of the inlet and outlet members, and maintains a substantially constant volumetric flow of liquid dispensed from the elastic member.