Abstract: In order to research the failure prediction and post-failure constitutive model of rock under triaxial stress, the triaxial compression tests of limestone and sandstone were conducted under different confining pressures, the regularities of deformation and failure and the relationship between strength and deformation in the whole loading process were analyzed. Based on the test result, a constitutive model for rock was founded. The research results show that the failure mode of limestone is stability loss under a low confining pressure condition, and high confining pressure can restrain rock burst to some extent. The circumferential strain corresponding to the peak stress is nearly a constant under different confining pressures, as a result, it can be taken as an index of rock failure prediction. The shear dilatancy occurs in the post-failure to limestone and at the moment when the axial stress reaches 70% of the peak stress to sandstone. The stress of rock is equal to its strength in the post-failure state, controlled by the lateral deformation, and decreases to the residual strength as the lateral deformation increases. The calculational results based on the constitutive model are consistent with the experimental results under triaxial compression.