Flexible foams have unique properties that make them well-suited to several engineering systems. They are often used in impact-related applications because of their superior energy absorption performance. Many multifunctional materials are also derived from flexible foams due to their high customizability, which allows them to satisfy a wide range of performance requirements. Though flexible foams have high potential in these and other classes of material applications, their success relies on the proper characterization of their complex behavior. This thesis promotes the application of flexible foams by characterizing their electromechanical response through both experimental and theoretical approaches. One study in this thesis theoretically determines material indices that minimize a foam's mass and cost while meeting particular energy absorption requirements. These novel indices are combined with a common Ashby approach to facilitate materials selection of energy-absorbing foam components. Another study uses a particular multifunctional nanocomposite foam to experimentally determine deviations in its voltage response while under a cyclic impacting regime; specifically, factors of transient effects, environmental conditions (humidity and temperature), and permanent material degradation are investigated. Results presented in this thesis promote the application of flexible foams to various forms of impact-absorbing sports equipment (specifically football helmet pads and gait-sensing shoe insoles), but are also useful in various other engineering designs.