An intravenous fluid pump (IV) contains a disposable part including a fluid chamber having a resilient top membrane and a non-disposable part including a piston abutting a resilient membrane and a vacuum chamber fitted on top of the resilient top membrane. An external pump is used to create vacuum in the vacuum chamber, resulting in the resilient top membrane being held taut. The flow rate through the pump is relatively independent of changes in the pressure of IV fluid on the upstream and the downstream due to changes in the relative elevation of the fluid reservoir and the patient with respect to the fluid pump.