The linear and nonlinear optical susceptibilities of unreconstructed and reconstructed (2×1) Si(111) clean and hydrogen covered surfaces were studied by application of an ab initio approach, namely the self-consistent full potential linearized augmented plane-wave method within the local-density approximation. The components of the susceptibility tensor for the clean surfaces calculated as a function of the incident photon energy reveal prominent features in the energy range below 2 eV which are attributed to optical resonances associated with surface states. The calculated data are consistent with previous experimental and theoretical works. An ab initio technique was used to derive the second harmonic response as a function of the polarization angle of the incident light. The polarization angle dependence of the calculated second harmonic intensity of (2×1) Si(111) agrees well with experimental data which could now be interpreted.