Fredholm’s integral equations of the second kind are formulated to describe the anomalous skin effect in metal films on dielectric substrates. An algorithm for numerical solution of equations based on the quadrature method is developed. As a result of its application to the processing of experimental data on the spectral ellipsometry of gold films of various thicknesses on a silicon substrate known from the literature, the density, relaxation time of the electron gas and the dielectric constant of gold are determined unambiguously. It is shown that the dependence of the dielectric constant of gold films on their thickness, noted in a number of experimental studies, can be associated with the use of the Drude’s normal skin model, which does not take into account the excitation of a space charge in the film. Optical fields in gold films are studied at different probabilities of specular reflection of electrons from the film boundaries. It is shown that among sensors of biological solutions with the Kretschmann configuration, structures in which the probability of specular reflection of electrons from the metal film-liquid interface tends to 1 are preferred.