Abstract: Taking stiffness of test machine as finite value, the mathematical model of damaging process in rock specimen, which is established by the energy balance principle, can be sorted into the fold castastrophe model. The model, including parameters of energy importing rate J and system stiffness ratio K , can properly describe the jumping instability or brittle damaging phenomenon that may occur and other phenomena that are recorded in the test when rock and reinforced concrete members damage under different loading ways. It can also analyze the stability of the system and provide theoretic basis for the servo control loading principle.