We have developed a time-domain staggered-grid finite-difference code for modeling non-linear response of a one-dimensionally inhomogeneous subsurface structure to a SH plane-wave incidence. It employs the velocity-stress formulation of elastodynamic equation for the linear part, and adopts a elastoplastic rheology model for the non-linear relation between the stress and strain. In this paper, we apply this code to four constitutive models from linear-elastic to nonlinear: (1) linear elastic model, (2) linear viscoelastic model, (3) elastoplastic model, and (4) viscoelastoplastic model, which simulate shallow sand and clay structures and are vibrated by a vertically incident SH plane-wave of Ricker wavelet, to compare the linear and the non-linear soil behaviors including low strains damping (viscoelastic effect) and/or hysteretic attenuation (non-linear effect). We also apply it to a local strong-motion record of the 2000 Western-Tottori earthquake (MW6.8). We then simulate characteristics of non-linear site response such as reduction of the spectral amplitude in the high frequency band and shift of the peak frequencies to lower frequencies.