In this thesis we use a new numerical code, based upon a mixed FEM-Runge-Kutta method, for the analysis and the design of plane 2-dimensional smart structures. We applied the developed code to the study of arbitrarily shaped piezo-electromechanical (PEM) plates. This code is based on a weak formulation of their governing equations as found in [18]. The optimal parameters needed to synthesize the appropriate electric networks are computed, and the overall performances of such plates are investigated. In particular, two examples are studied: firstly, a simple case is used to test the main features of the code; secondly, a more complex PEM plate is designed and analyzed by means of the proposed numerical approach.