The problem of scattering of electromagnetic waves by two-dimensional, randomly rough surfaces is solved by means of a mean-field theory. The results are compared with available numerical simulations and perturbative solutions. It is found that the new method is accurate for surfaces with a dielectric constant lower than 5 and roughness of up to half a wavelength. There are no limitations on the slopes. The explicit form of the result permits us to analyze in simple terms the polarization and angular scattering pattern of the diffuse intensity. It is shown that the angular scattering pattern depends not only on the correlation length but also on the rms height Δ, when Δ is greater than one tenth of a wavelength. Finally, the theory is used to analyze the scattering pattern produced by a rough film above a mirror. ¿ 1999 American Geophysical Union