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A lumped-parameter model is derived for flexural plate wave (FPW) devices which are rectangular plates or diaphragms with structural layers, a piezoelectric layer, and with interdigitated conducting combs for driving and sensing. This configuration is often used in micromechanical chemical sensors. The model is based an a closed-form solution of a resonating beam; however, the results are applicable to plates supported on four edges. The model gives a voltage or charge output from the sense combs as a function of voltage applied to the drive combs. The analysis predicts the response of the multiple plate modes to axial tensions and to comb finger dimensions and position relative to the diaphragm eigenfunctions. These models are much more detailed than those described in the literature on acoustic chemical sensors and are difficult to obtain by finite-element solutions. Frequency responses of FPW devices constructed from silicon with deposited aluminum nitride as the piezoelectric compared well with analytic results. The effects of boundary conditions on the plate's lateral edges are discussed in both the analysis and testing.