A Green's function approach is used to analyze mutual coupling in a finite array of different-sized rectangular waveguides arranged on a rectangular grid. In calculating the self- and mutual admittances for mode coupling, a quadruple integration over the source and observer apertures is involved. Possible means of reducing the order of integration are discussed, with the change of variables approach (due to Lewin) being selected. This approach is generalized to allow coupling between different-sized apertures, and leads to derivation of mutual admittance expressions for all possible combinations of transverse electric (TE) and transverse magnetic (TM) mode coupling. Calculations using these expressions are shown to be in good agreement with results published earlier by Mailloux and measured data for an antenna comprising a square waveguide and two rectangular waveguides. Coupling between closely spaced different-sized square waveguides is investigated also, and for small apertures minimum coupling is shown to occur when the aperture sidelength is about 1.15 λ.