The significance of stochasticity in the characteristics of the surface layers of a site to the resulting spatial variation of seismic ground motions and the seismic ground strains is investigated. For this purpose, an analytical site-specific model is developed. The model approximates the site topography by a horizontally extended layer with random characteristics overlaying a half-space （bedrock）. The spatial variation of the incident motion at the bedrock-layer interface incorporates the effects of the loss of coherence of the motions at increasing separation distances and their propagation in the bedrock; the site contribution to the spatial variation of the surface motions results from the vertical transmission of shear waves through the stochastic layer. It is shown, in an example application of the approach, that the spatial coherence of the motions on the ground surface is similar to that of the incident motion at the bedrock-layer interface except at the predominant frequency of the layer, where it decreases considerably. It is also shown that, for soft soil conditions, the layer stochasticity controls seismic ground strains. In the absence of spatially recorded seismic data at a site, the approach can be utilized for the description of the spatial variation of the motions in the seismic response analysis of buried and above-ground lifelines.