Vascular bypass procedures using traditional prosthetic grafts such as polytetrafluoroethylen (PTFE) and polyethylene tetraphthlate (Dacron) are prone to failure when used in low flow states such as in below knee bypass and when the diameter of the graft is less than 6 mm. A major factor in this is compliance mismatch between the graft and the diseased vessel, which may cause intimal hyperplasia at the distal anastomosis. PTFE and Dacron are rigid grafts with poor compliance. By improving the compliance of the prosthetic graft it is hoped that patency will improve. Recent advances in polyurethane chemistry have developed materials that do not degrade and which allow compliance matching of the graft to the patient's vasculature. It is now possible to manufacture biologically and haemodynamically compatible grafts with small diameter from these polyurethane graft materials. This review will focus on the lack of compliance in current vascular bypass grafts and the promise of the new polyurethane polymers in a new generation of small-bore bypass grafts.