The reflected and refractive fields are calculated for a very rough surface which is assumed to be a set of tangent planes with small corrections due to the local finite radii of curvature. A perturbation technique similar to those used in the moderately rough surface calculations is developed to treat the solution for the tangent planes as the unperturbed solution with the curvature correction as the perturbation. Our results are expressed in terms of the slope distribution function of the tangent planes and the average radius of curvature. Numerical results for scattering of both polarizations are obtained. The depolarization calculation is shown to be consistent with the experimental data. Further, the relationship between the surface model and the conventional Gaussian model is discussed, and a comparison with previous works is given.