Abstract: The study on strength theory of unsaturated soil is the core of the research in the field of unsaturated soil mechanics. In the early time, Bishop's univariate strength theory and Fredlund's bivariate strength theory are the most classical strength theories for unsaturated soil. Both introduce the matric suction as stress parameter. However, it attributes to effective stress in the former and it is an independent variable in the latter. Matric suction controlled unsaturated triaxial or direct shear apparatus are needed in order to get the related parameters in the two formulas. The controlling of matric suction needs synchronized increase of pore air pressure and pore water pressure so as to keep the matric suction constant, which is so called axis-translation technique. However, problems such as long process and its feasibility doubts still exist in axis parallel translation technique. Therefore, conventional triaxial CU test with different moisture content is used to get the effective steady state strength parameters. Then the suction stress characteristic curve is obtained on the basis of the suction stress concept. The shear strength formula is expressed as a function of suction stress which significantly avoids the determination of matric suction. Therefore, it is convenient for widely application in engineering practice. In order to make a further compare with the unsaturated strength of Bishop and Fredlund, the soil water characteristic curve of the same sample determined by tensiometer is used to get their strength parameters. In theory, these three strength theories are different in the mechanism explanation, but they can transform to each other in mathematics. From the perspective of engineering applications, shear strength theory, based on suction stress, is more convenient to apply in engineering.