Abstract: The failure of rock under triaxial compression is due to the localization of narrow shear band. Based on triaxial compression tests, local strains of a marble specimen are measured in present paper so as to study the development of the localization during the failure of specimens. Experimental results showed that the process of failure could be divided into three stages, that is steady stage, steady increase stage and quick development stage. The localization began to steadily increase before the volume of specimen dilated. When it accumulated to a higher degree, the specimen began to shear and dilate after a short time of strain hardening.A preliminary analysis of the bifurcation behaviors discussed above (sliding lines et al.) was conducted in the application of symmetric groups bifurcation theory.