an endovascular graft includes a flexible graft body dimensioned for positioning within a body vessel and having an outer wall defining an opening therethrough , and an elastic polymer strip mounted to the outer wall of the graft body . the elastic strip is dimensioned to increase an effective strength of the outer wall to thereby facilitate support of the body vessel upon implantation of the graft body therewithin . the graft body is preferably bifurcated including a tubular body defining a longitudinal opening and first and second legs connected to the tubular body . the first and second graft legs each define a longitudinal opening in communication with the longitudinal opening of the tubular body . the tubular body and the first and second legs preferably include the elastic polymer strip . the polymer strip is dimensioned to extend substantially along the lengths of the respective tubular body and the first and second legs . the graft elastic polymer strip may be helically disposed relative to the graft body . the graft elastic polymer strip may comprise a biodegradable polymer . suitable polymers include may be selected from the group consisting of polyglyocolide , polylactide , and copolymers of glycolide and lactide . the graft body may include two sheets of graft material joined together with elastic polymer strip disposed between the two sheets of graft material . the elastic polymer strip may includes vascular medication for treatment of the patient . preferably , a plurality of elastic polymer strips helically disposed relative to the graft body .