The phase transition and melting curves of CaF2 are investigated by using the general utility lattice programme(GULP)via the shell model with molecular dynamics method.By calculating the entropy H(at 0K)and Gibbs free energy G*(at 300K),we find that the phase transition pressure from the face-centred cubic(fcc)structure to the orthorhombic structure is 11.40 GPa and 9.33 GPa at 0K and 300K,respectively.The modified melting point of the fcc CaF2 is in the range of 1650-1733K at 0 GPa.All these results are well consistent with the available experimental data and other theoretical results.We also obtain that the melting temperature of hihg pressure phase is 990-1073K at 10 GPa.Moreover,the temperature dependences of the elastic constants Cij,bulk module B and shear module G are also predicted.