A study of electron stimulated desorption has shown that the desorption cross sections for Ba-W(111) and Ba-W(110) differ by two orders of magnitude. An oscillatory dependence on electron beam energy is observed for the desorption cross section for barium on W(111). It follows from a comparison of the energy dependence of the desorption cross section and of the Debye temperature, that both the anisotropy and the oscillatory behavior are determined by vibrational processes which are developed in the substrate.