A system for coupling a vascular overflow graft or cannula to a heart pump. A pump pipe outlet is provided with an external tapered surface which receives the end of a compressible cannula. An annular compression ring with a tapered internal bore surface is arranged about the cannula with the tapered internal surface in a facing relationship to the external tapered surface. The angle of inclination of the tapered surfaces is converging such that the spacing between the tapered surfaces decreases from one end of the external tapered surface to the other end thereby providing a clamping action of the tapered surface on a cannula which increases as a function of the length of cannula segment between the tapered surfaces. The annular compression ring is disposed within a tubular locking nut which threadedly couples to the pump and provides a compression force for urging the annular ring onto the cannula between the tapered surfaces. The nut has a threaded connection to the pump body. The threaded coupling to the pump body provides a compression force for the annular ring. The annular ring has an annular enclosure space in which excess cannula material from the compression between the tapered surfaces to "bunch up" in the space and serve as an enlarged annular ring segment to assist holding the cannula in place. The clamped cannula provides a seamless joint connection to the pump pipe outlet where the clamping force is uniformly applied to the cannula because of self alignment of the tapered surfaces. The nut can be easily disconnected to replace the pump if necessary.