Abstract: Based on the two-dimensional coherency function, a asynchronous excitation power spectral density (PSD) model is established, in which the effect of two-dimensional coherency is considered. The relationship between amplitude, phase angels and PSD is obtained using stochastic process. The numerical simulation method for the history of ground motions is proposed. With the proposed method, an acceleration history sample can be generated and used in the seismic response analysis of long-span bridges.