An extension to a previous approach is presented in order to treat the 2D TM-scattering from a multiangular groove engraved in a perfectly conducting plane. The domain product technique is used to construct solution of the problem in the interior of the channel. The efficient field representation, adapted to studying composite cylindrical structures with polyhedral boundaries consisting of conducting parts and interfaces, is proposed. The sought-for quantities inside and outside the cavity are expressed in terms of the Mathieu function expansions. Boundary value problem is reduced to solving a system of infinite matrix equations of the second kind with respect to the expansion coefficients. The validity and efficiency of the approach have been checked and confirmed for the case of a rectangular groove. Examples dealing with the arbitrary cavities are presented.