A percutaneous system for bypassing a restriction in a native vessel of a mammal having an aorta includes providing a graft having a body portion with a first end, a second end and a lumen therebetween. An aperture is formed in the aorta. The graft is inserted into the aorta and the first end of the graft is connected to the aorta about the aperture in the aorta. An aperture is then formed in the native vessel distal of the restriction. The second end of the graft is connected to the native vessel about the aperture therein such that the lumen in the graft communicates with the aorta and the native vessel.