The coupled electrothermoelastic constitutive relations, representing the behaviorof piezo materials, are shown to be nonlinear when the polarization-electric field interaction effects are properly accounted for. Under static condition, the polarization-electric field nonlinearities correspond to a distributed body force and body moment. For time varying situations, polarization-electric field interaction exhibits a hysteresis effect. Using the nonlinear constitutive relations, alayer-by-layerfinite element formulation is developed for both static and dynamic analyses of smart plates including hysteresis effects. Linear and nonlinear analyses are carried out to study the effect of nonlinearity due to polarization-electric field interaction on the response of the smart plates. To validate the present formulation, the results of static analysis of a smart plate are compared with experimental data available in literature. It is observed that the P-E hysteresis effects show a friction-type damping in the dynamic response of the smart plate. Copyright © 2010.