A small, accurate, reliable and economical pump which is particularly useful in intravenous (IV) feeding includes a disposable pump chamber and a pump housing. The disposable pump chamber has an inlet, an outlet, and first and second flexible rolling diaphragm pumping chambers. First and second cylinders in the pump housing are positioned to receive the first and second flexible rolling diaphragms of the disposable pump chamber. First and second pistons are movable in the first and second cylinders, respectively. In addition, first and second valves are provided in the pump housing. The first valve controls fluid flow between the inlet and the first flexible rolling diaphragm pump chamber, while the second valve controls fluid flow between the first flexible rolling diaphragm pumping chamber and the second flexible rolling diaphragm pumping chamber. A motor and cam shaft drive the first and second pistons and the first and second valves. The first and second valves are controlled so that one valve is closed at all times, thereby providing fail safe operation of the pump.