An accurate numerical-analytical method of solution of the problem of wave diffraction by a perfectly conductive cylindrical body with a cross-section formed by crossing of the “key” elements (such as flat strips and cylindrical screens) is proposed. It is based on the ideas of the moment method and the partial inversion technique of the initial problem operator. For this problem, Gegenbauer polynomials form a complete orthogonal system of the basic functions. As a result, the initial problem is reduced to the solving of infinite systems of linear algebraic equations.