A formalism is introduced for the nonperturbative purely numerical solution of the reduced Rayleigh equation for the scattering of light from two-dimensional penetrable rough surfaces. As an example, we in this way study the scattering of p- or s-polarized light from two-dimensional dielectric or metallic randomly rough surfaces by calculating the full angular distribution of the co- and cross-polarized intensity of the scattered light. In particular, we present calculations of the mean differential reflection coefficient for glass and silver surfaces characterized by Gaussian and cylindrical power spectra. We find our results to be in agreement with previous work. The proposed method is found, within the validity of the Rayleigh hypothesis, to give reliable results. In particular, for a non-absorbing metal the conservation of energy is explicitly checked, and found to be satisfied to within 0.03\% or better for the simulation results presented.