The problem of scattering of flat linearly polarized wave on a system of absolutely thin ideally conducting fillets with parallel edges comes to two scalar boundary value problems [1]. It is Dirichlet's problem (in the case of a falling E-polarized incident wave) and Neumann's problem (in the case of H-polarization) for the two-dimensional Helmholtz equation on a system of segments located arbitrarily (Fig. 1).