The increasing urban population is leading to the exploitation of building sites, close to surface or underground railways, with considerable levels of ground-borne vibration. An important design consideration regards the levels of perceptible vibration and/or re-radiated noise in the completed buildings. A fundamental question concerns to what extent the mass and stiffness of a building foundation influences these levels. This paper explores this question in relation to a concrete slab foundation. Previous research has explored the influence of the coupling between a thin, flexural plate and an elastic half-space on the free-surface displacements arising from surface Rayleigh waves. Here, a numerical, wave-based approach is used to model the slab foundation as an elastic layer of finite thickness, overlying the half-space. The latter is subjected to incident waves in the form of Rayleigh, P- and SV-waves. It is found that thin-plate theory alone is insufficient for modelling the slab over the full frequency range of interest, and that the assumed soil-slab boundary condition plays a significant role. Design plots are presented in order to summarise the influence of the salient dimensionless parameters, and to help guide the design of a slab foundation to achieve a specific reduction in ground vibration level.