Shear strength parameters are most important factors to evaluate the stability and economical efficiency of a geotechnical project. One of the most effective and mainly used ways to estimate the shear strength parameters is linear regression method. The shear strength parameters can be calculated either by regressing maximum shear stress with average normal stress or regressing maximum principal stress with minor principal stress. The equations to apply these two methods are introduced

These methods and moment method are applied to calculate the shear strength parameters of core clay in Xiaolangdi Dam with 320 triaxial tests and clay of several other embankments; and the results show that the cohesive strength is underestimated and friction strength is overestimated by regressing maximum shear stress with average normal stress will the standard deviation and relation coefficient decreased when the sample size increased. The theoretical analysis also reveals this trend. The theoretical analysis based on probability also reveals that trend. So the method regressing maximum principal stress with minor principal stress not regressing maximum shear stress with average normal stress should be chosen when estimating shear strength parameters from conventional triaxial tests.