This invention is a method of using a medical device. The device is a foldable stent or stent-graft which may be percutaneously delivered with (or on) a catheter, typically an endovascular catheter, to a body cavity or lumen and then expanded. The expandable stent structure utilizes torsional members which distribute bending and folding loads in such a way that the stent is not plastically deformed. The stent's configuration allows it to be folded or otherwise compressed to a very small diameter prior to deployment without changing the length of the stent. The graft component cooperating with the stent is tubular and preferably is blood-compatible material which may, if desired, be reinforced with fibers. The stent is able to provide collapsible support for otherwise frangible graft material. When used with super-elastic alloys, the stent may be collapsed at a convenient temperature either above or, preferably, below the transition temperature of the alloy. The deployment procedures may involve the use of an outer sleeve to maintain the stent or stent-graft at a reduced diameter or may involve one or more external or internal "slip-lines" or "tether wires" to hold and then to release the device.