An important factor in system longevity is service-phase evolvability, which is defined as the ability of a system to physically transform from one configuration to a more desirable configuration while in service. These transformations may or may not be known during the design process, and may or may not be reversible. A study of 210 engineered systems was performed and found that system excess and modularity allow a system to evolve while in service. Building on these observations, this thesis introduces mathematical relationships that map a system's excess and modularity to that system's ability to evolve. These relationships are derived from elastic potential energy theories. The use of the evolvability measure, and other related measures presented herein, are illustrated with simple numerical examples and applied to the design of US Navy nuclear aircraft carriers. Using these relationships, it is shown that the Navy's new Ford-class aircraft carrier is the most evolvable carrier designed to date. Though the evolvability relationships introduced here are generically derived based on excess and modularity, the aircraft carrier example presented considers only the system excess.