A glenoid component for a shoulder prosthesis adapted to be mounted in a glenoid cavity of a shoulder. An elongated keel adapted to engage with the glenoid cavity is attached to the internal surface of the base. The keel extends along a longitudinal axis of the base. The keel includes various configurations of transverse members extending away from the longitudinal axis. The surgeon selects a glenoid component with a keel and transverse member configuration that is anatomically optimized for the patient. Glenoid components properly optimized provide mechanical strength and stability superior to prior art devices. The glenoid components disclosed herein are particularly well suited for use in an anatomical total shoulder prosthesis, but may are also suited to partial shoulder prostheses and reverse shoulder prostheses.