The technological modes of annealing of the layered glass-metal composite material – glass-metal composite – which include heating-up to the glass softening point and aftercooling with annealing are investigated. The mathematical model of stress evolution is considered. The complexity in modeling is caused by the combined deformation of the glassy layer and the elastic-plastic layer with non-uniform temperature changes.  Structural and mechanical relaxation processes in the glass transition interval are described within the framework of the relaxation kinetic theory of glass transition. The algorithm for calculations of technological and residual stresses in glass-metal composite, at different modes, is proposed. A comparison of the numerical method with the analytical solution obtained for constant thermomechanical parameters of materials is presented. The practical implications are in the possibility of modeling technological and residual stresses in laminated structural cylindrical systems functioning during cyclic heating-cooling to high temperatures, including glass transition and plastic deformation of the layers.