An accelerated boundary integral method for the analysis of scattering of the dominant mode by multiple multi-layered full-height circular cylindrical posts in a rectangular waveguide is presented. After some transformations the surface integral equation is converted to a system of equations whose entries can be evaluated analytically yielding Schlömilch series. Slow convergence of these series is accelerated using the Ewald technique. The proposed method gives results that are comparable in terms of accuracy with other approaches, including those incorporated in solvers HFSS and CST Studio and outperforms them in terms of computation time, especially for posts with large electrical sizes. The efficiency of the proposed method is confirmed by the examples of H-plane cylinder bandpass filters design.