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.