Roller pumps are used in medicine to pump blood in extracorporeal blood circuits. Blood is subjected to mechanical stress in these peristaltic pumps, due to the complete tube occlusion. This stress causes damage to red blood cells (hemolysis). We present a novel peristaltic pumping principle that addresses these issues. In contrast to conventional roller pumps, the tube is stimulated by a circulating eccentric oscillation. Therefore, this type of pump does not require complete tube occlusion. The blood is less mechanically stressed and hemolysis is reduced by 55% compared to a roller pump.