This paper deals with with a piezoelectric solid under anti-plane mechanical and in-plate electrical load. The mathematical modeling of piezoelectric materials leads to rather complicated systems of initial-boundary value problems (IBVP) for coupled system of second order partial differential equations. The aim of this work is to study the behaviour of the solutions of above mentioned IBVP by means of resonant tunnel diode (RTD) based cellular neural networks (CNN) approach. The authors construct RTD-based CNN model and propose its numerical simulations. The application of Lyapunov majorizing equations method enables them to investigate the dynamics of the problem under consideration.