Autogenous saphenous vein is generally considered to be the best material for arterial bypass grafts below the inguinal ligament. Recent results have suggested that the advantage of vein over prosthesis is more pronounced in a distal situation, but it is not immediately apparent whether the difference is sufficient to justify a policy of using prosthesis for the initial above-knee graft to preserve the vein in case later surgery is required. An attempt has been made to answer this question. The literature has been reviewed to obtain estimates of the patency rates for grafts in different situations and a mathematical model has been set up using these figures to predict the outcome of different treatment policies. The model can be used to predict the result of alteration or inaccuracy in the data or to make use of the results of newly reported studies. The model predicts that the use of prosthesis for an initial graft will reduce the overall patency and substantially increase the requirement for reoperation, even if the present data give a substantial overestimate of the advantages of vein above the knee.