Idea of using piezoelectric materials with flexible structures made of rubber-like materials is quite novel. In this study a non-linear finite element model based on updated Lagrangian (UL) approach has been developed for dynamic response and its control of rubber-elastic material with surface-bonded PVDF patches/layers. A compressible stain energy density function has been used for the modeling of the rubber component. The results obtained are compared with available analytical solutions and other published results in some cases. Some results are reported as new results which will be useful for future references since the number of published results is not sufficient.