Discussions on the yield criterions of soils in low stress conditions were made. Some problems about composite yield criterions and shear yield criterion were pointed out. Based on the triaxial tensile test results and the mechanical characteristics of soils, “tensile-shear failure” was presented when existence of tensile stress in soils. The method that using convential shear strength indexs (c and ϕ) and uniaxial tensile strength ( σt ) to detemine strength indexs of tensile-shear failure ( σL and ϕL ) was presented. According to the characteristics of muddy clay in Shanghai, an extrusion-tensile device was designed to determine uniaxial tensile strength. Based on the test results, the strength indexs were determined.