Using the planar waveguide concept in surface acoustic wave (SAW) technology is often advantageous when the modeling of transversely distributed phenomena is indispensable for an accurate design of SAW devices. This is especially true when complex multi-track structures such as transversely coupled resonator filters (TCRF's) are under consideration where, e.g., transverse velocity and stiffness profiles have to be incorporated in the device simulation. The interdigital transducers (IDT's) and the reflector gratings composing those devices behave as planar waveguides supporting in principle all kinds of modes such as bound, semi-bound and radiation modes. Therefore, to model these SAW propagation effects, we subdivide the SAW structures in transverse direction into several parallel waveguiding channels (N regions), and take, as the wave-describing quantity, a two-dimensional scalar potential function. By doing so, we obtain a complete set of orthonormal modes into which an arbitrary transverse excitation function can be expanded in order to study its propagation. The general mode spectrum includes a discrete spectrum of bound modes and continuous spectra of semi-bound and radiation modes, respectively. We calculate all types of modes by making use of the stack matrix technique. The present work provides some results in the simulation of waveguides with N acoustic regions using the complete analysis of general SAW multi-channel structures presented in Reference .