By yielding under small inter-story deformation, hysteretic dampers installed to a response control structure absorb seismic energy and effectively control the damage to the frame. When designing such a structure, it is important to estimate the maximum deformation and the cumulative plastic deformation of the dampers against ground motions. Especially in the early stage of design, simple methods are useful for the preliminary study of determining the characteristics of the dampers. In this research, the shortcomings of the existing simple methods are discussed and a new method is proposed. Its accuracy and applicability are investigated using numerical examples.