Abstract: In order to study the problems of scattering by rough metallic surfaces, we have used Maxwell`s equations in covariant form within the framework of a non-orthogonal coordinates system adapted to the geometry of the problem. Electromagnetic fields are written in Fourier`s integral form. The solution is found by using a perturbation method applied to the smooth surface problem, this is fully justified when the defects are of small magnitude. For the direct problem, the mean value of diffraction intensity is obtained for random rough surfaces of finite conductivity by computer simulation. In the case of the inverse problem, the reconstruction of the profile of the metal surface from values of the diffraction intensity, obtained by simulation, is found using an iterative algorithm.