In order to solve the problem about determination of stability of dish solar concentrator system, a computational fluid dynamics software STAR-CCM+ is used to investigate the lift coefficient and the drag coefficient of the concentrator under different wind attack angles and height angles. Based on the simulation results of the lift coefficient and the drag coefficient of the concentrator, some main steps to can be expressed as follows: (1) A mechanical model of dish solar concentrator system under different wind attack angles and height angles is established and the moment equation of the dish solar concentrator is used as a potential function to establish the cusp catastrophe model of instability of a dish solar concentrator. The stability criterion based on the lift drag ratio Kid is proposed based on the bifurcation point set. If -1.54 < K-1d < 1.54, the system is stable. If K-1d = 1.54, the system is critically stable. If K-1d < -1.54 or K-1d > 1.54, the system is unstable. (2) The stability of dish solar concentrator system is determined, and the critical stability state of the dish solar concentrator system is achieved. The rationality of the method is verified by the pitch moment coefficient.