Optical properties of cubic semiconductor surfaces may be probed using experimental techniques which use crystal symmetry to exclude the optical response of the bulk senticonductor from the spectrum. Reflectance Anisotropy (RA) and Optical Second Harmonic Generation ,are examples of these techniques. The former is the linear optical technique where the reflectivity of a surface is measured as a function of frequency parallel and perpendicular to a symmetry plane perpendicular to the surface. The cubic symmetry of the bulk solid ensures that the bulk contribution to the RA spectrum is zero. The main effect which causes the RA from a semiconductor surface above the optical band gap is the difference in local fields for the two polarisations used in measuring the RA spectrum. Many-body theories ,are being applied to optical properties of electrons in solids, however they are expensive in terms of computer time when applied to systems with large unit cells, such as surfaces. One approach to calculating local fields in solids with a band gap is to adopt the classical, discrete dipole model where the response of a solid to an external field is given in terms of a local polarisability and the Lorentz local field. This is relatively inexpensive in terms of computer time and systems with hundreds or thousands of atoms per unit cell can be treated. This model has been applied to RA of five silicon surfaces which have been studied experimentally. It is found that the discrete dipole model gives a reasonably good account of the observed experimental spectra. Calculations of local fields and polarisabilities at silicon surfaces are also investigated using a quantum mechanical approach which employs a localised orbital basis set. The advantages and disadvantages in using a localised orbital basis for many-body calculations on systems with large unit cells vis-a-vis a conventional plane wave basis ,are considered.