Using a real-space multigrid method and ab initio pseudopotentials we calculated the reflectance anisotropy spectra for (001) growth structures of GaP and InP as well as for stepped Si(111):H and hydrogenated Si(110) surfaces. Our results, obtained within DFT-LDA, show good qualitative agreement with recent experiments. Further improvement is achieved by using a numerically efficient GW approach with approximations for local-field effects and dynamical screening. We find the contributions to the anisotropy signal related either directly to surface states or to transitions between surface-perturbed bulk wave functions. Our results demonstrate the high sensitivity of RAS to the surface structure and chemistry and show that the optical transitions causing the anisotropy signal take place mainly in a few uppermost atomic layers of the substrate.