The widespread use of graft replacement material led to complications inherent to these prostheses with increasing frequency. The discussion is still open on identifying those inherent features of vascular grafting that could contribute to long term success or short term failure. The search has been prompted for better arterial substitutes, among others, for repair particularly of lesions of smaller arteries. The ideal graft should have an innately blood-compatible flow surface with fixed endothelium and basement membrane and innately physiological mechanical properties. There are a number of biological and plastic materials competing for this goals. All plastic materials studied in clinical trials so far stimulate an uncontrollable proliferative response in host arteries behind or in the distal anastomosis; such causes failure of grafts when of small caliber. This distal anastomotic subintimal hyperplasia (SIH) is an ubiquitous pathologic entity in late graft occlusion. The cause of SIH has been the subject of much investigation. The role of compliance mismatch between host artery and vascular grafts in the development of SIH is discussed in this paper. While compliance may, in fact, be an important parameter in determining the results of bypass grafting, the dominant influence of hemodynamic and thrombogenic factors has continued to mask what is probably a very subtle effect. Summarizing the current knowledge it is likely that match or mismatch between the anisotropic behavior of the host artery and the linear respectively nonlinear response to varying blood pressure of the graft influences patency results. Any mismatch in tubular compliance in a quantitative manner will contribute to the long-term results but in a lesser degree. Disturbance of the biomechanical properties of the arterial tree due to an vascular anastomosis seems to be of utmost importance to the outcome, but up to now we were not able to demonstrate a link conclusively between compliance mismatch and the occurrence of subintimal hyperplasia. The present results imply a major impact on future graft design and the development of better anastomotic techniques, because compliance is a critical parameter for maintenance of arterial reconstructions.