A method for delivering and deploying a self-expandable heart valve to a site of implantation such as the aortic annulus. The deployment step may include engaging an outer surface of the heart valve with a plurality of distal fingers and a plurality of proximal fingers. Controlled radial movement of the fingers regulates the expansion of the heart valve. The fingers may be removed prior to inflation of a balloon to fully expand the valve, or the fingers may be repositioned to the inside of the valve for this purpose. The deployment step may include an umbrella structure that forces the valve outward into its fully expanded configuration. Alternatively, a gear shaft that engages one or more gear tracks on the valve may be utilized to regulate expansion of the valve. A stabilization balloon may be used to axially and radially locate the deployment mechanism relative to the site of implantation.