A vaulted diaphragm for providing occlusion in a descending thoracic aorta, includes a flexible and substantially circular element, and a plurality of resilient ribs having inner and outer ends supporting the circular element. The inner ends of the ribs are joined together at a hub with the ribs extending radially outwardly therefrom. The ribs are generally positioned on and attached to the circular element with the outer ends of the ribs having protrusions projecting radially beyond the circular element. The ribs have a resilient expansion tendency, such that the diaphragm may be held in a biased folded position during installation and sprung open into a normally vaulted shape upon installation in the aorta, whereby the protrusions are urged radially outwardly by the resilient expansion tendency of the ribs to engage the aorta and hold the diaphragm in position. A surgical procedure for treating an aneurysm in a patient's descending thoracic aorta, includes the step of installing an artificial aorta by-pass connecting the patient's ascending natural aorta with the patient's abdominal aorta end. A temporary graft is installed onto the by-pass and a catheter having a capsule end holding a diaphragm is advanced through the graft. The diaphragm is positioned into a selected site in the aorta, and then released by ejecting it from the capsule and the catheter is withdrawn, with the diaphragm remaining within the aorta to provide an occlusion therein.