We develop a model for the calculation of screening at the surface of single Ag crystals, including the response of both conduction and bound electrons. We obtain the electron-energy-loss spectra on the low index faces, and from it, the corresponding surface plasmon ͑SP͒ dispersion relations. Our results depend strongly on the face orientation and, for Ag͑110͒, and also on the propagation direction. With an appropriate choice of surface density profile for the conduction electrons, our model yields large positive SP dispersions, in qualitative agreement with experiment. ͓S0163-1829͑99͒11631-X͔ PHYSICAL REVIEW B 15 SEPTEMBER 1999-I VOLUME 60, NUMBER 11 PRB 60 0163-1829/99/60͑11͒/8348͑11͒/$15.00 8348There is also a coupling to the polarization p B e ϪQz m , consisting of a direct and a surface-mediated interaction. The former can be separated into a short-range contribution ͚ m e ϪQz m T J nm sr Ϸe ϪQz n T Jsr ͑24͒ and a long-range contribution ͚ m e ϪQz m T J nm lr ϭe ϪQz n ͑ T J Ͼ lr ϩnT J Ͻ lr ͒. ͑25͒Here we introduced the short-range interaction tensor 8352 PRB 60 CATALINA LÓ PEZ-BASTIDAS AND W. LUIS MOCHÁ N