In order to evaluate the surface stability during the development of underground holes, the process of surface displacement change during the development of the hole is discretized, and the criterion of surface collapse analysis is established according to the catastrophe theory. The validity of the criterion is preliminarily verified by combining the consistency of the cover instability，the simultaneity of instability, the plasticity penetration criterion and the plastic zone cloud map analysis. The above method is used to quantify the determination process of the surface instability so as to obtain the critical hole radius and surface collapse range. The relationship among the critical thickness of the cover layer, internal friction angle, cohesion, elastic modulus and Poisson's ratio is discussed. The results show that the thickness of the cover layer, the internal friction angle and cohesion can be fitted into a linear relationship with good correlation. The thickness of the cover layer is not sensitive to Poisson's ratio and elastic modulus. The criterion of surface instability based on catastrophe theory can provide a useful reference for the study of surface stability above the developed pore.