A modified four-parameter multi-axis equivalent strain damage model is presented based on a typical uniaxial tensile stress-strain curve model and four-parameter equivalent strain. To verify the concrete damage model, test results under six kinds of stress states, including uniaxial tension, uniaxial compression, biaxial tension, biaxial compression, biaxaial tension-compression, triaxial compression are compared with experimental results. With the concrete damage model, this paper numerically analyzed combined force situations of concrete shear tests and working performances of concrete gravity dams and concrete arch dams. The damage and stress distribution of these structures under static loadings are obtained and analyzed. The results showed that the numerical simulation results of shear tests coincide with experimental results. Therefore, the model can analyze the combined force situation with the shear as the main force and the model is suitable for the calculation under complex stress states. In addition, the reasonable damage and stress distribution rules of typical gravity dams and arch dams indicated that the model could analyze the working performance and safety of concrete dams.