The damage value of rock changes dynamically in the process of rock damage. By improving the Harris function,a damage constitutive model of rock under three-dimensional stress is established,and the parameters of the model are determined through triaxial test on sandstone. The relationships among confining pressure,critical damage value,and peak strain are analyzed qualitatively. Research results show that: 1) the model curve of sandstone’s damage constitutive model based on improved Harris function is well fitted with the measured curve,and has good applicability;2) the critical damage value is not a fixed value for the same kind of rock under different confining pressures,indicating that the mechanical properties of rock are related to its three dimensional stress state;3) the critical damage value increases correspondingly when confining pressure increases, which proves that confining pressure has a restraining effect on rock damage. The analysis results have a certain reference significance for the study of damage mechanism of rock under three-dimensional stress condition.