A volumetric pump for administering intravenous fluids to a patient comprises a housing having an elongate cavity therein with an open and a closed end. A resilient sheet of material having a centrally-located aperture covers the open end, and a pump shaft is slidably disposed through the aperture to form a sphincter seal therebetween. An inlet conduit leading from a fluid source (an IV bag) passes through the housing into the cavity near the open end thereof, and an outlet conduit leading to a fluid sink (the patient) passes through the housing from the cavity near the closed end thereof. The shaft is driven back and forth in reciprocating motion inwardly and outwardly of the cavity to produce, respectively, a positive pressure forcing fluid out of the outlet conduit to the fluid sink, and a negative pressure forcing fluid from the fluid source through the inlet conduit.