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The electromagnetic scattering from a cylindrical dielectric object of arbitrary cross-section buried in a lossy dielectric half-space having a periodic surface is investigated using a new numerical method. The method is outlined for TMz (horizontally) polarised incident wave. The surface equivalence principle and a decomposition method are employed to form a set of electric field integral equations (EFIEs) for the currents on the object and the portion of the surface most strongly interacting with the object. Then, the method of moment (MoM) is used to solve the EFIEs in the frequency domain to obtain the scattered electric field.