A bifurcated or straight intravascular folded tubular member is deliverable percutaneously or by small cutdown to the site of a vascular lesion. Its inserted state has a smaller nondeployed diameter and a shorter nondeployed length. The intravascular tubular member has a folded tubular section that is unfolded following insertion into the blood vessel. The length of the intravascular folded tubular member is sized in situ to the length of the vessel lesion without error associated with diagnostic estimation of lesion length. The folded tubular member is self-expandable or balloon-expandable to a larger deployed diameter following delivery to the lesion site. An attachment anchor can be positioned at the inlet or outlet ends of the intravascular folded tubular member to prevent leakage between the tubular member and the native vessel lumen and to prevent migration of the tubular member. The attachment anchor has a short axial length to provide a more focal line of attachment to the vessel wall. Such attachment is valuable in attaching to a short aortic neck in the treatment of abdominal aortic aneurysm. The attachment anchor can have barbs which are held in a protected conformation during insertion of the tubular member and are released upon deployment of the attachment anchor. The intravascular tubular member can be formed of woven multifilament polymeric strands with metallic strands interwoven along with them. Double weaving is incorporated to prevent leakage at crossover points.