A hemodialysis system has a blood circuit and a hemofiltrate circuit interconnected at a hemofilter and an air collection chamber. If an infusion of sterile fluid to the returning blood is needed during the dialysis treatment, filtrate in the filtrate circuit is pumped back into the blood circuit. This is also done to purge the blood circuit of blood and return it to the patient at the conclusiion of a dialysis treatment. A blood pump in the blood circuit incorporates a flexible vessel in conjunction with pinch valves which self expand in a controlled manner from a compressed condition to fill with blood from the patient in a suction stroke controlled by the patient's blood delivery rate. Compression of the vessel by an external member then forces the blood through the rest of the blood circuit.