A stationary power spectral model presented by Hu Yuxian is selected as a random earthquake excitation for base-isolated structures.The story hysteretic drifts of the base-isolated structures are described by Bouc-Wen model.The equivalent linearized state equation is established after equivalent linearization of dynamic property matrixes of hysteretic system.By introducing left and right eigenvector series

the vibration differential equation is decoupled and the analytical solutions of response statistical moments of structures are found.In accordance with the deformation failure criterion

the limit states of base-isolated structures are defined.On the basis of the first passage mechanism

the hypothesis about Possion distribution and the series connection reliability model

a simplified method for evaluating the seismic reliability of base-isolated structures on the whole is presented.Finally

a frame structure with base isolation is given for numerical illustration of the proposed method.