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In this work the applicability of the couplings-of-modes (COM) approach to the analysis of one- and two- port thin AIN film plate acoustic resonators (FPAR), utilizing the S0 Lamb wave, is discussed. Analysis based on the Fluquet-Bloch theorem as well as COM parameter extraction from a micromachined FPAR test structure are simultaneously used to verify the applicability of the COM approach. Subsequently, COM based design of 2-port FPARs for use in feed back loop oscillators and cascaded filters is demonstrated. The proposed theoretical approach can easily be adapted to the case of S0 Lamb wave resonators utilizing reflections from suspended membrane edges.