Abstract: The prothesis is intended to be implanted in a human patient for forming an aorto-coronary by-pass or another by-pass on other arteries. The prosthesis comprises a normal, unaltered living vein which is taken from the patient himself/herself and which is surrounded by a multiperforated flexible sheath. The inside diameter of the sheath is so chosen that, after implantation, the outside diameter of the vein is maintained by the sheath at a value less than the maximum possible diameter of the vein and that the inside diameter of the vein is suitable for the diameter of the receiver artery.