Based on statistical damage theory, the whole process of concrete damage evolution cumulative induced catastrophe was elaborated in detail from the perspective of effective stress, the internal relation between mesoscopic damage mechanism and macro mechanical behavior was analyzed. A statistical damage model of concrete under uniaxial tension and compression considering the influence of strength grade was established. Two mesoscopic damage models for fracture and yield were considered in the model, which was corresponded to the “deterioration” and “strengthening” mechanisms of microstructure respectively. The peak nominal stress state was distinguished from the critical state, and the critical state was used as the precursor of damage localization. The analysis results show that the model can predict the macroscopic stress strain behavior of concrete with different strength grades(C20 C80) under uniaxial tension and compression, and can reflect the influence law of strength grade on the mesoscopic damage evolution process of concrete. With the increase of strength grade, the characteristic parameters of the evolution process of mesoscopic fracture and yield damage show significantly regular change trend. The mesoscopic damage mechanism ultimately determines the macro nonlinear stress strain behavior of concrete, and the yield damage mode plays a decisive role in the whole process.