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In a flat and uniform site, it is reasonable to assume that the spatially varying earthquake ground motions at various locations have the same power spectral density or response spectrum. If an engineering site with varying soil conditions at different structural supports is considered, this assumption is no longer valid because of different local site amplification effect. This paper presents an approximate method to model and simulate spatially varying ground motions on the surface of an uneven site with non-uniform conditions at different locations in two steps. In the first step, the base rock motions at different locations are assumed to have the same intensity, and are modelled by a filtered Tajimi–Kanai power spectral density function or other stochastic ground motion attenuation models. The base rock ground motion spatial variation is modelled by an empirical coherency loss function. The power spectral density …