Excited near its resonant frequency, a thin transverse-type rectangular Piezoelectric Transformer with common ground electrodes (PTCGE) converse an electric voltage in driving part, providing mechanical vibrations and converted back to an electrical signal in the output part. They are dedicated to the systems of electronic or electromechanical that require voltage source boosted or bucked with good galvanic isolation for DC/AC or DC/DC converter commercialized in monolithic fabrication. Otherwise, problems are occurred in modeling, design and characterization of these devices. Approaches conducted on the transverse-type PTs are recently neglected the distance between the primary and secondary electrodes called « gap ». The finite element Approach (FEA) not allows appear the mathematical expressions in the structure and keeps high storage memory. In this paper, the Polynomial Approach is reported to this device for analyzing the free vibration modes and the electrical behaviors especially the gap dependence on the voltage gain letting the bottom surface completely covered with ground electrodes taking into account the gap. Then, a good agreement is found in our results through a comparison of those obtained with the FEA ones.