Аннотация:In this work we consider the problems of scattering of a monochromaticwave by a dielectric body in the form of a thin layer placed on a perfectly conductingbase. For this casewe formulate the boundary value problem forMaxwell’s equationswith an impedance boundary condition and reduce it to a system of two boundaryintegral equations with weakly and strongly singular integrals on a perfectly conductingsurface. Finally, we construct a numerical method for the considered problemwhich based on solution of these integral equations.