The generalized admittance matrix (GAM) approach to the analysis of cylindrical cavities coupled to external waveguides by rectangular apertures is discussed. Green's dyad of the admittance type under the longitudinal section electric (LSE) field approximation is derived and GAM is obtained by Galerkin's method. Several numerical results are presented and a criterion for the optimal mode selection is discussed. A reduced formulation having improved efficiency is derived and its use is critically discussed. Comparisons with results of mode-matching, finite-element method and with measurements are shown. The analysis is successfully applied to waveguide bandpass filter design.