An implantable prosthetic valve (100) has an in situ formable support structure. The valve comprises a prosthetic valve (104), having a base and at least one flow occluder. A first flexible component is incapable of retaining the valve at a functional site in the arterial vasculature. The first component (126) extends proximally of the base of the valve. A second flexible component (128) is incapable of retaining the valve at a functional site in the arterial vasculature. The second component extends distally of the base of the valve. At least one rigidity component (300) combines with at least one of the first and second flexible components to impart sufficient rigidity to the first or second components to retain the valve at the site.