Effects of compliance mismatch at end-to-end artery/graft anastomoses on the distributions of wall stresses and compliance were studied using the finite element method. The canine common carotid artery (CCA), and expanded polytetrafluoro-ethylene (EPTFE) thin-walled graft, and a newly developed polyurethane graft (HS-2) were used as the models for the host artery, stiff graft, and compliant graft, respectively. Mechanical properties of CCA and HS-2 were determined from a pressure–diameter test, those of EPTFE graft were obtained by tensile test. Nonlinear elasticity of CCA and HS-2 was incorporated by iterating a linear FEM analysis: elastic moduli of the vessel walls were changed every 5 mmHg. The results showed that, in the case of the artery/EPTFE anastomosis in which the diameters of the artery and the graft were matched at 0 mmHg, regions of high tensile and shear stresses appeared in the graft near the anastomosis at the intraluminal pressure of 100 mmHg. The stress concentrations were remarkable, even if the diameters were matched at 100 mmHg and the pressure was varied within a physiological range (60–140 mmHg). Moreover, a hypercompliant zone appeared in the arterial wall near the anastomosis in this case. On the other hand, neither high stress concentrations nor hypercompliant zone appeared near the artery/HS-2 anastomosis. Because the mechanical complications at the compliance-mismatched anastomosis might finally result in graft failure and occlusion, it is important to match the compliance of graft to that of natural arteries, particularly to improve the patency of small-calibered arterial grafts. © 1994 John Wiley & Sons, Inc.