A medical device for treatment of affection of anatomical ducts, as in particular for anastomosing blood vessels and vascular prosthesis, with end-to-end or end-to-side configuration. The device has outer containing functions and is associated to an intra-prosthetic stent for sandwiching the overlapping segments being anastomosed to each other of the anatomical ducts and of the prosthesis, a segment of which is located in the duct. The outer containing device is formed by a stent of biocompatibile resilient material having memory effect, in a predetermined nominal position, suitable for extending elastically for engaging the outside of the duct, and returning to said nominal position, with containing function, thus preventing the diameter of the duct from increasing and without compressing the duct. The stent must have at least a length not less than half the outside diameter of the duct. Means are provided for putting the prosthesis in the duct and for arranging the containing device out of the duct.