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For accelerated incompressible, ideal elastoplastic plates of finite thickness with a preformed sinusoidal perturbation at the interface, we investigate the stability behavior encompassing neutral and most-unstable modes, stable oscillatory modes, and the onset of plastic flow. We show that the largest perturbation wavelength that can maximize the growth rate corresponds to a finite thickness plate. For elastically stable configurations, stress gradients that arise as a result of the interfacial disturbance can lead to the formation of counter-rotating particle displacement trajectories that tessellate the extent of the plate. By computing the spatiotemporal evolution of the stress tensor, we are able to construct the boundaries that demarcate the transition from elastically stable oscillatory modes to the onset of plastic flow based on the von Mises yield criterion. Earlier estimates of these boundaries for thick plates differ qualitatively and quantitatively from the present results, in which the common simplifying assumptions of thin-plate theory were not invoked. We show that multimodal solutions are necessary to accurately represent the actual oscillatory behavior of the stress tensor, which in general is not time periodic, that thin-plate bimodal solutions are unable to capture.