This paper discusses simplified theories on cumulative damage evaluation for elasto-plastic damper under earthquake ground motion. The theories are based on the seismic behavior of single-degree-of-freedom (SDOF) elasto-plastically damped structure, cumulative plastic deformation of damper can be clearly expressed as a function of stiffness parameter, ductility demand, natural period of structure and duration of earthquake ground motion. The relationship between cumulative plastic deformation and maximum deformation is also clarified. Accuracy of proposed evaluation method is demonstrated via numerous time history simulations using a wide range of multiple-degrees-of-freedom (MDOF) models.