We consider the direct and inverse problems of electromagnetic scattering by cylindrical structures with arbitrary cross sections for Neumann, and impedance boundary conditions for line sources. In the case of impedance boundary condition we also consider scattering by electromagnetic plane waves. We present a method for approximately solving the direct and inverse scattering problem by applying the method of lines, which results in an efficient procedure for calculating scattering amplitude and also for obtaining satisfactory reconstruction of the shape of cylindrical structures if the far-field scattering amplitude is given. In the case of the impedance boundary condition the impedance of the boundary is also recovered. We present some realistic numerical examples, which illustrate the proposed procedure.
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