Abstract: The strength criteria of rock fragile fracture are discussed. According to the surface characteristics of rock ultimate strength in stress space, strength criteria of the twin and octahedral shear stress, which reflect the surface characteristics of rock ultimate strength, were applied to regression analysis of ultimate surface of rock strength. On the basis of data of true triaxial compression strength from experiment of red sandstone, the strength criteria of twin and octahedral shear stress with three parameters are recommended by the regression analysis for eight kinds of strength criteria.