The most general and accurate approach to analysis of multilayer structures presumes three-dimensional theory. We present the nonlinear dynamical equations of the three-dimensional theory of elasticity and the theory of thermoelasticity of multilayer shells subjected to thermal and force loading. The problems are considered in coupled and uncoupled statements. The results of solutions of three-dimensional equations of coupled problem of thermoelasticity for multilayer shells are practically not known. This is caused by the complexity of equations, which describe thermoelastic state of shells, and by the necessity to satisfy additional conditions at a large quantity of boundary surfaces, i.e. the conditions on the contact boundaries of layers. These circumstances complicate determination of the solution radically, particularly when using equations of coupled problem of thermoelasticity in displacements. In order to reduce the difficulties caused by the necessity to satisfy the conditions at layer contact boundaries, we choose unknown functions in such a manner that the conditions of compatibility of deformations of adjacent layers can be formulated in terms of these functions. The system of equations can be transformed to obtain the equations with respect to these unknown functions.