We developed an analysis system for simulating birefringence of an annealed ingot of CaF<sub>2</sub> single crystal caused by the
residual stress after annealing process. The analysis system comprises the heat conduction analysis that provides the
temperature distribution during the ingot annealing, the stress analysis to calculate the residual stress after ingot
annealing, and the birefringence analysis of an annealed ingot induced by the residual stress. In the residual stress
calculation, we can select either the elastic thermal stress analysis using the assumption of a stress-free temperature or
more exact stress analysis considering the time-dependent nonlinear behavior of a material called creep. When we use
the residual stress calculated from the creep deformation analysis of a CaF<sub>2</sub> ingot, we can obtain reasonable results both
for the optical path difference values and for its distributions in comparison with the experimental results.