Graft material attachment device and method

An attachment device (500) is described which comprises a deformable, partially tubular band (504) having a slotted opening for accepting a portion of a first substantially flexible element and a portion of a second substrate element (502). A stent graft (10) is also described which comprises: one or more stent structures; a biocompatible graft material affixed to the one or more stent structures; and at least one attachment device for securing the biocompatible graft material to the one or more stent structures. The stent-graft can be fabricated from a thin-walled, high strength material which provides for a more durable and lower profile endoprosthesis. The stent-graft can comprise one or more stent segments covered with a fabric formed by the weaving, knitting or braiding of a biocompatible, high tensile strength, abrasion resistant, highly durable yarn such as ultra high molecular weight polyethylene. The one or more stent segments may be balloon expandable or self-expanding. The fabric may be attached to the stent segments utilizing an attachment device that secures the fabric to a strut of the stent segment by sandwiching the fabric between itself and the stent strut.