Abstract: A new extra-vascular wrapping (EVW) is disclosed. The EVW comprises of a (i) wrapping adapted to at least partially encircle at least a segment of an aorta, especially an aneurysmatic aorta, and (ii) anchoring means located at the distal portion of the wrapping adapted to immobilize the wrapping to the aorto-iliac bifurcation via engagement of the aorto-iliac junction, wherein the bifurcation-anchored wrapping is applied external to the aorta and further wherein the wrapping is collapse-resistant in the proximal-to-distal direction of the aorta. The EVW is presented with its various embodiments, such as gusset-like structured EVW, Sustained drug delivery EVW, supported EVW and ringed EVW. Methods for treating aneurysmatic aorta in an open-surgery procedure by utilizing the EVWs and by applying step of positioning a macroporous medical textile externally adjacent to the aorta are also disclosed.