This paper summarizes our experience in designing and developing shape memory devices for compression anastomosis in the digestive system. Literature review and our own extensive experimental and clinical material have allowed us to formulate the medical and biomechanical demands for these devices, and to specify design requirements for accomplishing the optimal anastomosis. It is shown that the use of the unique thermomechanical features of the NiTi shape memory alloy enables us to resolve most problems of the existing suture-based (hand-sewn or stapled) and sutureless methods of anastomosis. As a result of the experimental research on the thermomechanical behavior of shape memory implants and the associated computer-finite element analysis, key principles of shape memory implant design for compression anastomosis have been established.