Abstract We calculate the binding energy of an exterior electron bound to an impenetrable metallic surface by its image potential. To describe the image state, we use a microscopic model, involving the coupling of the electron to dispersionless surface plasmons. This coupling is treated dynamically, in the framework of a Fock approximation derived from a Green's function approach. We find that, for an abrupt surface, the binding energy depends only on the frequency of the surface plasmons. Our results are compared with other theoretical treatments and with experimental data obtained for three transition metal (0 0 1) surfaces: Cu, Ag and Au.