Abstract: An anisotropic compressive damage model based on energy dissipation mechanism is developed to model the hysteretic behavior of concrete by introducing the nonlinear unloading/linear reloading branches into the conventional continuum damage model. The damage factor representing the stiffness degradation is defined as a function of the dissipating energy accumulated during loading histories. The model is applied to simulating a concrete test under cyclic compression and the influence of damage exponent  is also investigated. The results show that the stress-strain response calculated by the model is highly comparable to that obtained by the test. The numerical response reflects the nonlinear behavior of concrete under cyclic compression, e.g. the stiffness degradation, accumulation of residual deformation and hysteretic energy dissipation. Moreover, the value of damage exponent  has a remarkable influence on the computational accuracy. The numerical simulation shows that the model is applicable to analyzing the behavior of concrete under cyclic compression.