The calculation of residual stresses and deformations requires solving the energy equation for the cooling phase and the above equations for the nonisothermal elastic case. These differential equations require appropriate boundary conditions, and the transient character of the process requires the assignment of appropriate initial conditions as well. From the point of view of the energy equation, the initial temperature will typically correspond of that of the glass at the end of the forming process, before cooling. Cooling will usually occur via convection, which requires the specification of a transfer coefficient and an outside temperature.

The momentum equation (Equation 26–3) also requires initial and boundary conditions. Since it is often assumed that thermal stresses develop from a stress-free state, initial conditions are set to zero. The assignment of boundary conditions is less obvious and depends on the individual case. The most typical conditions will probably be symmetry, stress-free or displacement-free border, though other choices are possible.