Calculation of the surface dielectric function (DF) is an important issue for a proper description of many experiments. In this work we present a method for evaluating the DF in half-space geometry avoiding slab or supercell approximations. The method is based on Green's functions and requires no explicit knowledge of wave functions and energies. We test our method by calculating the DF of GaAs(110) and show results for the reflection anisotropy spectroscopy signal.