Abstract: The strength theories of geotechnical materials can be classified as single shear strength theory, tri-shear strength theory and twin-shear strength theory. They are represented by the Mohr-Coulomb theory, Drucker-Prager criterion and the twin-shear theory respectively. Each strength theory has its own representative element model. The strength theory is established by analyzing the stresses that cause the model element to fail and by developing the mathematical relationship among the stresses on the model. Based on the characteristics of failure and strength of rocks under symmetry compression tests and true tri-axial compression tests, the authors introduce a new twin-shear model and associated strength theories for rock materials.