The present disclosure provides aortic valve prosthetic devices that are constructed in a non-axisymmetric shape, or are expandable to a non-axisymmetric shape for improved results in the repair of defective aortic valves. The devices can be surgically implanted, or they can be implanted percutaneously through an insertion catheter. The expandable devices can be self-expanding or expanded by an inflatable balloon to a non-axisymmetric cross-section geometry.
