In this work the applicability of the coupling-of-modes (COM) approach to the analysis of thin AlN film plate acoustic resonators (FPAR), utilizing the S0 Lamb wave, is discussed. Analysis based on the Floquet-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. Finite element model simulation is used to further study the contribution of the higher order mass loading effects over the Lamb wave propagation under a periodical grating. A possibility to achieve zero sensitivity of the FPAR resonance with respect to the grating strip thickness is identified and physically interpreted for the first time.