Indentations on the main crystallographic plane (111) of CaF2 were analyzed. Appropriate material parameters were obtained by experiments. The process of CaF2 indentations had been investigated by the finite element approach in order to obtain the initial shear yield strength. The results show a value of 110 MPa for the initial shear yield strength. Vickers hardness of plane (111) was also investigated. The results show the dependence on the orientation of the CaF2 crystal. The hardness is small at the angular direction 0° and 120°, and at the angular direction 60°, the hardness of the largest value is 1.67GPa. The Young’s Modulus and Fracture Toughness are also obtained. These properties are valuable to the ultra-precise machining of CaF2 crystal.