The results from the molecular dynamics simulations on crystalline, superionic, molten and quenched-amorphous states of calcium fluoride system are reported. The Ca++ and F- sublattices are studied by using the method of bond order parameters. The result shows that both Ca++ and F- sublattices can be described with the bond-orientation normal distribution model. In the superionic phase the Ca++ cations keep their original stable fcc frame, but in the F- case random distortion generates from their original simple cubic (sc) structure. The simulation on the molten phase gives three radial distribution functions that are difficult to separate from the experimental X-ray diffraction data. The simulation of quenched-amorphous state shows that a dense random packing of equivalent spheres centered by Ca++ cations occurs in the system simulated. However, the system quenched is not stable enough because the Ca++ cation and F- anions around it do not form themselves into a certain configuration. The results from the molecular dynamics simulations on crystalline, superionic, molten and quenched-amorphous states of calcium fluoride system are reported. The Ca ++ and F-sublattices are studied by using the method of bond order parameters. In the superionic phase the Ca ++ cations keep their original stable fcc frame, but in the F-case random distortion generates from their original simple cubic (sc) structure. The simulation on the molten phase gives three radial distribution functions that are difficult to separate from the experimental X-ray diffraction data. The simulation of quenched-amorphous state shows that a dense random packing of equivalent spheres centered by Ca ++ cations occurs in the system simulated. However, the system quenched is not stable enough because the Ca ++ cation and F-anions around it do not form themselves into a certain configuration.