Calcium fluoride has an appropriate change of refractive index and permeability of wavelength so that it is utilized for lenses, prisms or windows. It has been fabricated using conventionally grinding and polishing combined with interferometry and local surface correction to form the desired flat, sphere or aspherical surface. On the other hand, cutting is also necessary to make another complicated shapes such as diffraction grating. In this study, crack initiation on the (100), (110) and (111) planes of Calcium Fluoride are examined by micro-Vickers hardness tests. In addition, brittle-ductile transition is investigated by performing an orthogonal cutting test with ultra-precision machine tool. The results of these tests show that the critical depth of cut remarkably changes on the basis of the crystal orientation on each plane. We have discussed these changes from the viewpoint of slip system and cleavage.