The Martin's method, which is used to obtain the internal displacement of atomic systems and elastic constants, is applied to the Tersoff potential. The potential is modified to provide a good description of the high-temperature elastic properties of silicon. The elastic constants of crystalline silicon were investigated at both low and high temperatures. Results were verified by the statistical thermodynamic method'Fluctuation formula'. It was found that elastic constant values and the influence of the internal displacement are valid. However at high temperatures, the gap becomes larger owing to the thermal fluctuation. Since the convergence of the Martin's method is faster by about two orders, it is the more effective method. It was also found that the fluctuation term includes the effects of the internal displacement and thermal fluctuation.