In this paper, a mathematical model describing the dynamic behavior of a commercial piezoelectric ceramic, vibrating in thickness, is presented. This model solves, by finite differences, the piezoelectric equations which relate he mechanical and electrical phenomena produced in this kind of material. The behavior in time domain of some physical variables, as the electric field and particle velocity, is simulated too. In addition, we have implemented a GUI in Matlab that allows simple and affordable simulations for all users. The implemented interface provides two kind of study: Broadband and single frequency excitation. The output parameters, obtained after time domain simulation, are piezoelectric constants of the ceramic and the electric response in frequency domain, i.e. admittance and impedance curves. The results allow predicting vibration modes, electrical response and understanding the effect of piezoelectricity on the mechanical response.