Abstract: Discussions on strength theories were made deeply.The Mohr-Coulomb’s shear yield criterion was anatomized.Based on the criterion,the stress paths of tri-axial compression and tension tests with ordinary tri-axial instruments were depicted intuitively in the 3D principal stress space(plane of tri-axial instrument) and in the deviatoric plane and the meridional plane of the maximum and minimum principal stresses.The stress paths under the condition of plane stresses were also depicted.Considering soils as a material with weak or no tensive strength,the composite yield criterion of tension and Mohr-Coulomb’s shear and the composite yield criterion of tension,shear and volume were proposed to analyze the yield or failure behaviors of soils.The stress paths of loading and unloading in existing finite element methods were also discussed by using the composite yield criterion of tension and Mohr-Cloulomb’s shear.