Abstract: In this paper, four yield criteria, i.e. Tresca yield criterion, Mises yield criterion, Mohr-Coulomb yield criterion and Drucker-Prager yield criterion are categorized into shear yield criteria. Tresca yield criterion and Mohr-Coulomb yield criterion belong to the shear yield criterion for the shear stress and the normal stress at the critical plane of a given material point. Mises yield criterion and Drucker-Prager yield criterion belong to the shear yield criterion for the comprehensive measurement of shear stress and normal stress of all planes of a given material point. Based on the concept of ODF (Orientation Distribution Function), mean shear stress and mean normal stress are taken as a comprehensive measurement of shear stress and normal stress at all planes, which are defined as the average shear stress and the average normal stress at all planes respectively. For virgin isotropic materials, mean shear yield criterion states that the material will yield if the linear combination of mean shearstress and mean normal stress reaches an utmost value. It is shown that mean shear yield criterion has the same form as the Drucker-Prager yield criterion. Particularly, it has the same form as the Mises yield criterion if the effect of mean normal stress on yield is not considered. For anisotropic damaged materials, the mean yield criterion is the linear combination of the mean effective normal stress and the mean effective shear stress. The amplification ratios of the effective normal stress and the effective shear stress to their nominal counterparts are approximated by two-order fabric tensors. The mean yield criterion for the anisotropic damage material is expressed as quadratic equation of stress tensor components. For coordinates that coincide with the principal axes of the fabric tensors, it has been proved that the anisotropic yield criterion has the same form as the extended Hill anisotropic yield criterion. Particularly, if the effect of mean normal stress on yield is not considered,the anisotropic yield criterion has the same form as the Hill anisotropic yield criterion.