A stent (10) has wrapped therearound a barb element (12) formed of a length of wire provided with first and second ends (14, 16) forming barb prongs. In intermediate zone (22), the barb element (12) is wrapped or coiled. The two pronged ends (14, 16) extend out of the graft element (26) to provide an anchoring function to the medical device. As well as being wrapped onto a strut of the stent (10), the barb element (12) is sutured to the stent (10) and to the graft material (26) by suture stitching (28). The turns of the coiling or wrapping in section (22) assist in fixing the barb element (12) relative to the suture (28) and thus to the stent graft (24). The barb elements (12) could be made of any suitable material, including Nitinol. This structure of barb elements provides an effective arrangement which is easy to manufacture, which provides strong barbs able to withstand the high processing temperatures required for setting shape memory elements of the device.