The most prevalent form of ionic polymer metal composites used for actuation applications is that of thin strips or membrane/plate structures where the through-thickness dimension is much smaller than the other two. In this chapter, we exploit a multiphysics theoretical framework for developing the modeling infrastructure that can account for the nonlinear large deflection deformation of such structures under the influence of mechanical, electrical, thermal and multicomponent mass transport fields. The derived system of partial differential equations generalizes the well-known von Karman equations of large deflection plates originally developed for deflection under mechanical loads. We demonstrate the numerical solution of the system by using the finite element method for the case of a rectangular plate. In addition, we employ an inverse method for determining the analytical solution of the system of equations provided experimental data of the behavior of the plate are available. Finally, we apply the method to a square plate and demonstrate the applicability of the approach.