A three-stage model is introduced to describe the tensile failure process of rock and concrete materials. Failure of the material is defined to contain three stages in the model, which include elastic deformation stage, body damage stage and localization damage stage. The failure mode change from uniform body damage to localization damage is expressed. The heterogeneity of material is described with strain strength distribution. The fracture factor and intact factor, defined as the distribution function of strain strength, are used to express the fracture state in the failure process. And the distributive parameters can be determined through the experimental stress-strain curve.