Abstract：The paper demonstrates that the rock dynamic destabilization and the destabilization of geometry form of the elastic body are two essentially distinctive phenomena，which correspond to different catastrophe models. The mistakes existing in the research of rock dynamic destabilization by using catastrophe theory are pointed out. For the stabilization of elastic body with equilibrium branch point，some concepts and main points in the solution of total potential energy function are expounded. For rock dynamic destabilization without equilibrium branch point，in which the system equilibrium relation can be expressed with quasi-static displacement on the stage before and after the period of rock system coming into destabilizing，the equilibrium relation of work and energy increment can be established according to energy conservation principle. The equilibrium relation of work and energy increment is different from that of potential energy function. The equilibrium equation of catastrophe model that corresponds to the destabilization question of rock system can be deduced by the equilibrium relation. All main characteristics，demonstrated by the equilibrium equation and the equilibrium curved surface，is of one-to-one correspondence to the primary characteristics of destabilized prototype.
