In this article, we present a refined mathematical model of the stress–strain state of multilayer composite cylindrical shells taking into account the piezoelectric effect. The displacements and the electric potential of the shell are represented as polynomials in the normal coordinates two degrees higher in comparison with the classical Kirchhoff–Love type of theory. A mathematical model of the electromechanical state of composite shells is obtained using the variational Lagrange principle. The formulated electroelasticity boundary value problem is solved by reducing three-dimensional equations to two-dimensional ones. An example of calculating the stress state of the boundary layer type of composite cylindrical shells with symmetric and asymmetric distributions of layers under the action of arbitrary mechanical and electrical loads is treated taking into account the piezoelectric effect.