Two-dimensional finite element models have been used to study Rayleigh-wave propagation in two laterally inhomogeneous structures. The first model is a two-dimensional analog of a one-dimensional structure found for a basin of the Rio Grande rift; the second model is a modification of the first, to take into account a lateral variation known as the Hubble Bench. Both models are perfectly elastic. Two-station phase velocities and amplitude ratios were calculated from the complex displacements of nodes at the free surface for frequencies between 0.040 and 0.250 Hz. For both models, the phase velocities are 0.04 to 0.05 km/sec greater than the phase velocities calculated by averaging the slownesses from laterally homogeneous models. The introduction of the Hubble Bench causes a decrease in the amplitude ratios with frequency, a variation that could easily be misinterpreted as being caused by a near-surface layer or layers of high intrinsic attenuation. In addition, the results show that lateral variations in structure do not have to occur between stations in order to have a significant effect on both phase velocities and amplitudes, and that these effects may well be systematic rather than random.