This invention is a medical device and a method of using it. The device is a foldable stent or stent-graft which may be percutaneously delivered with (or on) an endovascular catheter or via surgical techniques or using other suitable techniques. The expandable stent structure utilizes at least one torsional member having an undulating shape which is helically deployed to form the generally cylindrical shape used as the stent. The helical winding desirably is aligned to allow those undulating shapes in adjacent turns of the helix to be in phase. The adjacent undulating shapes may be held in phased relationship using a flexible linkage, often made of a polymeric material. The stent may be flared on at least one of its ends to promote smooth blood flow at that flare and to assure that the stent will remain in the chosen position within the body. The stent's configuration allows it to be folded or collapsed to a very small diameter prior to deployment without changing the length of the stent. The stent may be expanded with the use of an installation device such as a balloon but preferably is used as a self-expandable device.