The laser host materials undergo relatively small changes in their intrinsic properties due to various sources during an experiment. These sources are often related to temperature change or applied stress, which may cause stress-induced birefringence. Consequently, the crystal experiences an optical anisotropy, which may affect the final outcome of the experiments. One way to reduce probable noises is to predict the change in optical properties with respect to load. To predict the changing pattern of the refractive index in a crystal, one needs to know both the elastic and photoelastic constants of the material. In this study, We utilized density functional perturbation theory (DFPT) to extract the photoelastic tensor of Y2SiO5 and Eu-doped Y2SiO5 crystals. Using the photoelastic and elastic constants calculated, a Finite Element (FE) model was developed, which allowed us to apply load and then post-process the results. This methodology enabled us to observe the variation in refractive index (n), and consequently, the shift in the resonance frequency of the cavity. The results obtained were in agreement with experimental measurements, falling within a 2% discrepancy across a temperature range spanning from cryogenic to room temperature. This correlation suggests the feasibility of using the current workflow as a predictive tool for evaluating variations in refractive indices over a specific interval.