An intraluminal graft/stent includes a hollow tubular member with inner and outer wall members defining a cavity in which is positioned a time-delay, heat-activated material partially filling the cavity. Upon implantation of the graft/stent in the blood vessel to be repaired, the time-delay, heat-activated material will foam and expand to completely fill the cavity causing the outer wall to sealingly engage the interior wall of the blood vessel. The inner wall, upon expansion, provides a conduit for the flow of blood. Under one embodiment, a flexible support member encircles the outer wall member and, by virtue of its shorter length and smaller cross-sectional size than the outer wall member causes enlarged cuffs to be formed at opposing ends of the graft/stent upon completion of expansion of the time-delay, heat-activated material.