Abstract: The article provides a new way of site response analysis using staggered-grid finite difference approach. To complete the site response analysis by simulating the wave propagation in soil, and the variables of stress and velocity represent the characteristics of site. At last, to analyze some non-linear one-dimensional site and to compare the result obtained by the staggered-grid finite difference technique with those obtained by lumped-mass method and SHAKE. The results show that the method of staggered-grid finite difference is useful for analysis of site response.