The achievements of rock and soil mechanics research have been obtained until now. A zipper type transducer is used to measure the radial deformation of a cylindrical sample of traditional triaxial test, in fact; it is assumed that the failure type of testing sample is symmetrical; it is reasonable for the failure to occur by “X” type or along the symmetrical axis of sample. The physical significance of the slope between the average stress (or deviatoric stress) and volume strain relationship doesn’t existed, but it is existed under the condition that an equivalent loading or unloading in the three directions is performed at the same time. Yield proportional limit stress and peak stress keep constant under elastic segment; when an applied stress is greater the yield proportional limited stress, the yield proportional limited stress and peak stress spaces are changed with the damage state; the load and displacement relationship is a comprehensive representation of mechanics and structure of material post-failure, the stress and strain must be changed to be defined as “quasi-stress and quasi-strain”. Traditionally, it isn’t reasonable for the areas of hysteresis to present the energy dissipation of rock and soil material under cyclic loading-unloading case; it is reasonable for the areas of hysteresis to behave the storage, conversion and dissipation of energy. Based on the mechanism analysis, a traction stress criterion must be suggested to describe the failure along the symmetrical axis of testing samples, that is rational to explain the fissure existence in the natural integrated rock mass. It is more reasonable for the material parameters to determine by the linear segment of unloading curve; a formula is suggested to classify the linear segment. When applied stress is greater than yield limit stress, a non-drainage test is performed for the porous interconnection material; the water pressure unloading is conducted to be near zero at a stress state; the material parameters can be obtained by means of linear segment of water pressure and strain curve. A hexahedron testing sample (50 mm×50 mm×100 mm) is suggested to take the place of cylinder. The damage variables keep constant within the yield proportional limited stress, when the applied stresses are greater the yield proportional limited stress, the damage evaluation is different in the different main stress directions, and is changed with stress paths.