A low profile, implantable prosthesis includes (a) a tubular graft including opposed open ends and having yarns in a textile pattern to define a textile wall having a luminal surface and an exterior surface; and (b) a tubular, radially extensible member including a portion arranged in a closed zig-zag pattern, the pattern having a series of angled bends at proximal and distal ends thereof, and longitudinally extending members having opposed proximal and distal ends, the distal ends being disposed from the angled bends of the proximal end; the longitudinally extending members having a plurality of detents for securing the yarns within the textile pattern at one of the opposed open ends, wherein the yarns of the textile patterns are securably disposed to the detents. The detents may be holes, inwardly extending notches, outwardly extending protuberances, or combinations thereof in the longitudinally extending members. The textile pattern of the graft may be a braided textile pattern, a woven textile pattern, a knitted textile pattern, and combinations thereof. Desirably, the zigzag portion of the radially extensible member is disposed beyond the open end of the graft. The radially extensible member may be a stent or may be an anchoring device for securing the prosthesis against the wall of a bodily lumen.