An implantable prosthetic valve having an in situ formable support structure and methods of deploying such a valve are disclosed. In one arrangement, the valve has a base and at least one flow occluder. A first flexible component which is incapable of retaining the valve at a functional site in the arterial vasculature extends proximally of the base of the valve. A second flexible component which is incapable of retaining the valve at a functional site in the arterial vasculature extends distally of the base of the valve. At least one rigidity component 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.