Abstract The undulation pump is a unique continuous-flow displacement-type blood pump with high performance. However, the undulation pump has limited mechanical durability. To eliminate this limitation, the principle of the rotary undulation pump was developed. The rotary undulation pump is composed of a disk having a pair of convex shapes on both side and pump housing having a shape such that one side is narrow and the other side is wide. The disk nutates and at the same time rotates at half the speed of nutation. With this movement of the disk, the disk can rotate through the narrow part of the pump housing and pump mechanism occurs. Between the disk and the pump housing, four pump rooms are created. The four outputs are added at the outlet port, and continuous flow is generated. The practical shape was designed with computer graphics. The motion of the disk was calculated accurately with the computer, and the principle was confirmed. The inlet and outlet port areas were also calculated. Models were developed to demonstrate the principle. With the magnetic coupling method, up to about 6 l/min of output could be measured against 100 mmHg of pressure load, and the principle was demonstrated to work. An experimental model to study an electromagnetic drive method, including a magnetically suspended drive, is being developed for the next step. Although many objectives remain, the basic principle of the rotary undulation pump was confirmed.