Abstract: Hysteretic dampers have been widely used in the reactor coolant piping system as the energy absorbing components.In the paper,the random seismic response is evaluated through the pseudo-excitation principle incorporated with stochastic equivalent linearization method without by solving the Lyapunov differential equation for which the seismic excitation at support is limited to be shot noise process.It is supposed that the structures keep elastic and the hysteretic dampers are represented by the versatile Bouc-Wen model.With the aide of assistant matrices,the unidirectional and spatial excitation vectors of three components are derived and a pseudo-excitation closed-form expression for the system random response is established.Consequently,the stationary random seismic response of two shear type structure interconnected with hysteretic dampers is analyzed.The structural root mean square displacement responses for two methods agree well.Meanwhile,the parametric studies for initial yield force of the hysteretic dampers and the optimum way to install the hysteretic damper are discussed.