The deviation from Cauchy's relation and the difference between the electrostaticand the optical dielectric constant for calcium fluoride are calculated respectively by usingKun Huang's method. The results of neglecting the electronic polarization in the ionic crystal are given as follows: c12-c44=0.58×1011 dyne/cm2, ε- ε0 = 3.53. The results of considering the electronic polarization in the ionic crystal are c12-c44=3.97×1011 dyne/cm2,ε - ε0 = 10.1. The experimental values are c12-c44 = 2.01 × 1011 dyne/cm2,ε - ε0 = 6.44.