A two-dimensional beam is scattered by a cylinder buried below a slightly rough surface. The cylindrical wave approach is applied, i.e., cylindrical waves are employed as basis functions of the fields scattered by the cylinder. Moreover, a spectral representation of both the incident field and the cylindrical waves is used. Rough surface deviation is coped with by the first-order small perturbation method. Therefore, to a zeroth-order solution relevant to scattering in the case of a flat surface, a first-order approximation is superimposed. The theoretical approach has been implemented for a periodic surface with Gaussian roughness spectrum.
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