The paper addresses some aspects connected with computational methods involved in analysis of shielded microstrip circuits in the frame of the IE-MoM approach. The paper is focused on a method for efficient evaluation of double infinite modal series, which arise in the analysis of vertical metallizations embedded in a waveguide or cavity filled with a multilayer medium. Generally, the modal series converge very slowly, when treated in its original form, and from practical point of view it makes the IE-MoM approach inefficient. The rate of convergence of the modal series can be significantly increased by means of a transformation of the double infinite series into a fast converging single series. The transformation exploits the contour integral and the residue theorem method in conjunction with the well known Kummer's transformation. The proposed method proved to be very efficient since it enables radical savings in computational time and this feature makes the method a good candidate for practical purposes, specially for electromagnetic CAD tools.