"ENDOVASCULAR SUTURE STAPLE", a component utilized for fastening a medical device to the wall of a blood vessel or inside a hollow body organ, may be specifically utilized for fastening vascular grafts on vessel walls, by means of endovascular sutures, comprised of a straight segment on the anterior end or front portion with its end trimmed to a wedge shape or pointed, and the posterior end(12) has a plain, straight, transversal section.