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A very efficient method for the accurate analysis of arbitrarily shaped H-plane two-port structures in rectangular waveguide technology is presented. The method is based on the integral-equation technique, which makes use of the Green's function of an infinite line source placed inside two parallel plates. All the terms of the series of the Green's function are analytically integrated, thus resulting in new series with accelerated convergence. After performing an exhaustive convergence analysis, optimal values for the parameters of this new method have been found and used in all calculations. The new method has been successfully tested after analysing several practical H-plane structures, such as inductive filters including the mechanisation effect of rounded corners.