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In this paper, we describe two multimode network representations for the analysis of radiating array of thick parallel plates. Due to periodicity and infinite extent, only one period of the structure needs to be studied. The key step is then the derivation of the equivalent network representation for the transition from a free-space region limited by phaseshift walls to a parallel plate waveguide. Two solutions to the problem are discussed. In the first solution, the relevant boundary value problem is cast into a network form that leads to an integral equation. The equation is then solved with the method of moments (MoM's). In the second solution, the elements of the multimode coupling matrix representing the grating are evaluated directly in terms of their network definition. The two solutions are then compared and the relative merits are discussed. The main feature of the approach presented in this paper, is that once the network representation of the key transition is obtained, it allows for the study of a wide class of scattering problems involving, for instance, corrugated surfaces and single or cascaded thick gratings. Comparison with published data are also presented, indicating that the two network representations developed are indeed very accurate.