The mechanism of earthquake energy input to connected building models on flexible soil is clarified. The earthquake input energies to super-structures, connecting dampers, soil-foundation systems and total system are obtained by taking the corresponding appropriate free bodies into account and defining the energy transfer functions. It has been made clear that, when the soil becomes softer, the effectiveness of connection dampers decreases. This phenomenon can be confirmed by the change of properties of energy transfer functions. It has further been disclosed that the maximization of the area (input energy to connecting dampers) of the energy transfer function for connecting dampers is a good index for determination of connecting damper quantity.