In the process of designing and using the geological drilling tools, strength theory or yield criterion is required to analyze drilling equipment and tool failure problems. In order to help people understand Mises yield criterion (stress), this paper introduces theoretically the relationship between the Mises yield criterion and the distortional strain energy density criterion, it is revealed that the essence of Mises yield criterions is the fourth strength theory. In the elasto-plastic range, Mises yield criterion unifies the first strength theory of the single tension or compression state, the third and fourth strength theory of complex stress state. Thus Mises yield criterion is more widely used in the finite element numerical analysis.