Reflectance anisotropy spectroscopy (RAS) offers extreme surface sensitivity and can be used to study gas-solid and solid-liquid interfaces. Although the technique has already made a considerable contribution to in situ monitoring of the epitaxial growth of semiconductors, its impact has thus far been Limited by difficulties in interpreting experimental results. In particular, RAS spectra are related to both Delta epsilon(2)' and Delta epsilon(2)'', the real and imaginary parts of the surface dielectric anisotropy, with weighting factors determined by the complex dielectric function of the substrate. Here RAS calculations are performed for a variety of substrates assuming a model overlayer dielectric anisotropy. Three distinct regimes of behavior are observed : RAS spectra can resemble either Delta epsilon(2)', Delta epsilon(2)'' or -Delta epsilon(2)'' (or some combination of the three) depending on the substrate and the photon energy. It is therefore crucial to properly account for these substrate effects if RAS is to be used to determine the azimuthal orientation of adsorbates or to Study the symmetries of surface states, for example. Similar considerations also apply to the related technique of surface differential reflectance. The Fresnel-based theoretical method used here and the substrate optical functions presented should serve as a useful database for future work as RAS is applied to new systems.