Abstract: Traditional Statistical Energy Analysis (SEA) theory can not deal with dynamic problem concerned with non-conservatively coupled systems. In this paper, based on the theory of power flow between and energy distribution in non-conservatively coupled oscillators, equations of power bal-lance and those for each concerned power flows and other power item calculations are derived to develop SEA theory for non-conservatively coupled systems. Results show that conservative coupling is only a special case in non-conservative coupling situations, the effects of coupling damping on power flow and energy distribution in non-conservatively coupled systems are not negligible unless the coupling damping is much small compared with internal damping. As an application of the theory, energy problems of non-conservatively coupled plates are studied theoretically and experimentally.