| Based on elastic strain energy, it is assumed that Poisson’s ratio is 0.5 in yield of the material, which may be one of the important reasons for the poor calculation precision of the MC strength criteria. Therefore, based on the fact that releasing of elastic strain energy is the essential attribute of material yield, the internal relations between elastic strain energy, the second invariant of stress deviator, and the second invariant of stress tensor and Poisson’s ratio are explored. Consequently, the generalized second invariant of stress deviator is proposed. Secondly, MC strength criteria are set as the basis, and the generalized MC strength criterion is established based on energy release and material yield. Lastly, the failure strength is calculated using strength criterion. The results show the generalized MC strength criterion is more accurate and the error is more stable because of the consideration of Poisson’s ratio and the intermediate principal stress. The generalized strength criterion breaks the hypotheses that Poisson’s ratio is always 0.5, which is of great significance for accurate quantitative analysis of failure characteristics of the material.