Zinc-oxide-based thin-film bulk acoustic wave (BAW) resonators operating at 932 MHz are investigated with respect to variation of dimensions of a boundary frame spurious mode suppression structure. A plate wave dispersion-based semi-2-D model and a 2-D finite element method are used to predict the eigenmode spectrum of the resonators to explain the detailed behavior. The models show how the boundary frame method changes the eigenmodes and their coupling to the driving electrical field via the modification of the mechanical boundary condition and leads to emergence of a flat-amplitude piston mode and suppression of spurious modes. Narrow band suppression of a single mode with a nonoptimal boundary frame is observed. Reduction of the effective electromechanical coupling coefficient k2eff as a function of the boundary width is observed and predicted by both models. The simple semi-2-D plate model is shown to predict the device behavior very well, and the 2-D finite element method results are shown to coincide with them with some additional effects. Breaking the resonator behavior down to eigenmodes, which are not directly observable in measurements, by the models, yields insight into the physics of the device operation.