Abstract: To calculate the stationary stochastic seismic response of coupled structures interconnected by hysteretic dampers subjected to non-uniform random seismic excitations,a pseudo excitation method based on the multi-support and multi-component was proposed.As the unknown quantity is not the dynamic relative displacement but the absolute displacement,the proposed method can be suitable for all the seismic excitation including uniform seismic excitation.Numerical research shows that:results from the proposed method,traditional pseudo excitation method based on the dynamic relative displacement and the Monte-Carlo numerical simulation method agree well,verifying the reasonableness of the proposed method.Further,parametric study of hysteretic damper about the yielding force and the yielding displacement is also developed.