Abstract: This paper deals with stability of a deployable flexible structure.It is resulted that the motions of the structure include the attitude motion,dimension motion and flexible vibration;the dynamics of the structure can be described by using hybrid partial differential and ordinary equations.It is proved that the dissipation and accumulation of the vibration energy depends on the dimension motion:in deploying phase the energy is dissipated and in retracting phase the energy is accumulated.Thus,it is concluded that vibration motion of the structure is stable in deploying phase and unstable in retracting phase.