Abstract: The main rock stress failure criteria and their applicability are introduced and it is necessary to study the deformation failure criterion. Based on the stochastic medium, the deformation failure criterion of stochastic medium is put forward. It can avoid complex constitutive law and can be expressed only with strain. It can reflect the inherent deformation properties of the rock and soil and can be used to estimate the engineering safety by use of the field observed data. Furthermore, the strain failure criterion is used to analyze the stability of a slope in Australia which shows that the theoretical results and the field observed data are consistent. The positions of slide plane with different slope angles are obtained with the present method, which are similar to the results of the limit equilibrium method. However, the deformation failure criterion of stochastic medium is simpler and more convenient in the engineering application because it is basd on the observed data and deformation control, which is not necessary to assume slide planes to compute its safety coefficient respectively.