A stochastic damage constitutive model is proposed based on Kelvin spring-damper model and Li Jie spring stochastic damage model. The model is made up by microscopic spring-slipper element. The slipper, parallel connected with spring, is introduced to consider the plasticity effect of concrete. Damage failure process of concrete subjected uniaxial tension is divided into spring broken state and slipper broken state to describe the elastic stage and plastic stage of damage respectively. In the light of energy conservation during the process of damage failure, stochastic damage constitutive equation of concrete material subjected to uniaxial tension stress is derived. Comparisons between test results and theoretical calculation results verify that the established constitutive damage equations are accord with the experimental situation, and the experimental data are observed undulated with theoretical curve in the range of variance. The research results can apply in the actual engineering.