<p>Mathematical model for describing and optimizing the thermal and stress states of semitransparent bodies under external thermal radiation is proposed. It is based on the relations of the phenomenological theory of irradiation in the approximation of nonradiating material and quasi-static thermoelasticity. The stages of statement of the optimization problems are considered, and various systems of constraints and optimality criteria are proposed. As an example, the optimal thermal stress state of a hollow gas-filled sealed glass sphere under external thermal radiation from the external spherical surface is determined and investigated. The optimal control function is found numerically using methods of the gradient (subgradient) projection, ravines, and local variations.</p>