A non-classical mathematical model of thermoelastic deformation of layered composite shells and plates is presented. It is based on special distribution laws for components of the displacement vector and the heat flow through the shell thickness. It takes into account transverse shear deformation and nonlinear temperature distribution across the thickness of laminated package to satisfy the conditions of ideal thermal, kinematic, and structural coupling of layers, thermomechanical loading conditions on boundary surfaces of the shell, coupling conditions of deformation fields and temperatures. A novel functional in the Laplace-transform domain is developed which uses three-dimensional thermoelasticity problem equations as the Euler equations of corresponding variational problem. With the assumptions made, the functional is reduced to the two-dimensional functional, and differential equations and boundary conditions of coupled thermoelastic deformation problem of layered composite shells and plates are formulated for the Laplace-transform domain for further inversion.