Surrounding rock system of underground engineering is highly nonlinear, and there is no unified cognition for its stability criteria. A simplified mechanical model for the surrounding rock is built , considering the influence of the water，introducing water weakening function, using the cusp catastrophe theory，the necessary and sufficient mechanics criterion of the surrounding rock is obtained, and the critical radial displacement of deep buried tunnel instability is obtained. In practical engineering，it is show that catastrophe theory is a feasibility method to study the instability problem of the Deep buried tunnel.