In recent years, seismic evaluation and design techniques which are able to evaluate cumulative damage have been required. Authors have dealt with this issue from the viewpoint of the energy balance equation. The energy balance equation expresses cumulative information of response, so that the energy balance equation is adequate for the evaluation of the influence of cumulative load such as seismic response. Authors have already clarified qualitative relationships between input energy and fatigue failure of simple single degree of freedom system. However, in order to apply energy balance equation on actual structure for seismic evaluation, expansion of it to multiple degree of freedom systems is required. Therefore this paper proposes three types of energy balance equation for multiple degree of freedom systems, that is a matrix method, an each mass method and a modal method. Energy balance equation by the matrix method indicates energy of a whole system. The equation by the each mass method indicates energy of each mass. The equation by the modal method indicates energy of each mode. In this paper, behaviors and features are investigated by numerical simulation and vibration experiment.