Continuum damage mechanics is used to model the damage induced by a thermal shock to the R7T 7 glass, the French borosilicate glass used for nuclear waste vitrification. A finite element model of the thermal shock is developed in which the elastic constitutive equations are coupled with an anisotropic stress-based damage evolution law. The Weibull distributions of strength measured at various temperatures by biaxial flexural tests are used to identify the parameters of this damage evolution law. Vibration tests are conducted to identify the elastic properties of the glass and to determine the effect of thermal shockinduced damage on the glass residual stiffness. The residual stiffness predicted by the damage model agrees with that measured experimentally. The fractured surface in the glass after a thermal shock is estimated, assuming that all the elastic energy associated with the stresses that are higher than a pre-determined threshold is dissipated in the creation of new surfaces. Comparison between the predicted and experimentally-measured fractured surface is performed. The model is shown to capture the saturation of the crack network density for severe thermal shocks; whereas this is not the case if damage is not accounted for in the constitutive equations.