Residual strength of rocks is an important parameter in rock mechanics, because it has a significant influence on accurately evaluating stability of underground excavations and optimizing design of rock mass support. Based on triaxial mechanical properties of the rock, an index, defined as the strength degradation coefficient, is proposed to describe the post-peak strength degradation of rock. In this paper, the index is in essence a brittle index for rocks. A power model is then proposed for the relationship between the strength degradation coefficient and the confinement stress. By fitting the data from 22 lab triaxial compression tests, it is found that the parameters in the model which are different in various rocks can be mainly related to the mineralogical composition and the structure of rocks. Furthermore, a strength degradation method based model is proposed for determining the residual strength of rocks. It is found that the proposed model fits triaxial compression test data of rocks better than the classical Mohr-Coulomb failure criterion does. Meanwhile, it can reflect the influence of structural properties on the residual strength of rocks.