<p>By using the modified Hu–Washizu variational principle, we obtain an inhomogeneous three-dimensional system of equilibrium differential equations. The application of this system makes it possible to study the stress-strain state of a composite cylindrical anisotropic shell for the force and temperatures impacts specified on its end faces. The anisotropy of the material of the shell is characterized by a single plane of elastic symmetry in each layer. By the Bubnov–Galerkin method, the original threedimensional system of equilibrium equations is reduced to a one-dimensional system of first-order ordinary differential equations with respect to the radial coordinate. The obtained boundary-value problem is solved by the numerical method of discrete orthogonalization. We present the results of numerical analysis of the stress-strain state of an anisotropic cylindrical composite boron–plastic shell protected against the action of high-intensity temperature fields by a layer of a nanoceramic functionally graded material.</p>