This paper develops a system of 2D shear deformable equations so as to analyze the non-linear vibrations of shells on the basis of the 3D fundamental equations of thermopiezoelectricity with a second sound effect. First, a differential type of variational principles is presented for the 3D fundamental equations. Next, the system of 2D approximate equations of successively higher orders is deduced from the 3D fundamental equations with the aid of the variational principle and the series expansions of the field variables of thermopiezoelectric shells. The system of 2D equations which is established in invariant differential and variational forms governs all the types of vibrations of thermopiezoelectric shells at both low and high frequencies. All the mechanical, electrical and thermal effects of higher orders are taken into account for the case of large electric fields, infinitesimal temperature variations and large deflections. Lastly, attention is confined to some of special cases involving types of vibrations, geometry and material properties. Besides, the uniqueness is investigated in solutions of the system of fully linearized 2D equations of thermopiezoelectric shells and the conditions sufficient for the uniqueness are enumerated. (C) 2002 Elsevier Science Ltd. All rights reserved.