Abstract: Based on the description and Analysis of the deformation process and the forms of fracture for undisturbed soil samples taken from the core of an earth dam in tri-axial tensile tests, this paper presents that there are three different failure forms of the soil samples under different cell pressure. （ 1 ） pure tensile fracture, （ 2 ） shear and elongation at first, tensile fracture followed, （ 3） pure shear failure. The formula generally used to calculate the tensile strength is effective only for the first form. For the second form, considering the influence of shear in the sample, a formula to calculate the true tensile strength is developed. For the third form, the tensile strength from the triaxial tensile tests can not be obtained.