We are interested in non-destructive electromagnetic characterization of disorganized periodic composite materials composed of a multi-layer infinite plate with a periodic set of circular cylindrical fibers in each layer. The work presented is the preliminary analysis of the scattering of a single-layer plate. An approach based on the multipole method and plane-wave expansion is proposed for obtaining the field representations in all regions of space and forming the formulas for the calculation of reflection and transmission coefficients. To confirm applicability and accuracy of the proposed method, various numerical examples are given when the plate is illuminated by a plane wave.