In the present work, a fast and robust method to analyze multiple cylindrical posts with multiple cylindrical inclusions is developed and discussed. The cylindrical posts are located in a rectangular waveguide. The method employed herein is a boundary integral method discretized by entire domain basis functions. The resulting surface integrals can be evaluated in closed form, except those over the outer surfaces, which result in very slowly converging series of cylindrical functions. A considerable speed-up in the convergence of these series is achieved by means of well-established Ewald's summation technique. To verify the efficiency of the developed method numerical studies were performed. The calculated results for several different configurations are compared with the data obtained using Ansys HFSS. Owing to its semi-analytical nature, the method requires several orders of magnitude less CPU time than FEM based Ansys HFSS.