Abstract: A rock damage constitutive model with consideration of residual strength is established,based on the strength of rock micro elements and the Weibull distribution law, and the damage variable correction factor is discussed.Using multivariate functions to obtain the extreme values,the theoretical expressions of model parameters \(m\) and \(F_0\) are derived with consideration of correction coefficients. The model consists of an addition of a linear term of correction coefficients; the correction factor \(\delta\) reflects the characteristics of the residual strength of the rock, to improve the accuracy of the modified constitutive model with an appropriate value of \(\delta\).