We propose a fast and accurate full-wave code capable of analyzing electrically large substrate integrated waveguides consisting of stacked parallel-plate waveguides hosting dielectric or metallic posts and coupling and/or radiating slots. Boundary conditions enforced on posts yield scattering amplitudes, while slots are modeled by equivalent magnetic currents, solved by a method of moments. Substantial accelerations are proposed to exploit various symmetries of the structures and to select the optimal number of modes according to the relevant geometrical and physical parameters. The formulation is validated by full-wave simulations with a commercial software and measurement results.