This paper brings up the module of time delay stability analysis. The author establishes the time delay dynamics equation of force reflection telepresence system, and then analyzes the time delay stability of force reflection telepresence system in the elastic environment by using the system of differential and differences equations. Furthermore, this paper discusses the effects of the parameters in the model and defines the limits of time delay. At the end of this paper, a case is simulated to verify the correctness of this module.