The paper presents an efficient two-dimensional approach to piezoelectric plates in the framework of linear theory of piezoelectricity. The approximation of the through-the-thickness variations then considered accounts for the shear effects and a refinement of the electric potential. On using a variational formalism the fully electromechanically coupled plate equations are obtained for the generalized stress resultants as well as for the generalized electric inductions. The latter are, in fact, deduced from the conservative electric charge equation which plays a crucial role in the present model. The emphasis is also placed on the boundary conditions on the plate faces. The model is then used to examine some problems for the cylindrical bending of a single plate simply supported. In this configuration a number of situations are examined : a piezoelectric plate subject to (i) an applied electric potential, (ii) a surface density of force and (iii) a surface density of electric charge. The through-thickness distributions of electromechanical quantities (displacements, stresses, electric potential and displacement) are obtained and compared to the results provided by finite element simulations and by a simplified plate model without shear effects as well. A good agreement is observed between the results coming from the present plate model and finite element computations, which ascertains the effectiveness of the proposed approach to piezoelectric plates.