Abstract: A new damping model is presented and combined with the elastoplastic damage constitutive model previously proposed for concrete by the authors.To inherently consider the energy dissipation at the material scale,an effective damage stress is introduced,and damping stress is obtained within the framework of continuum damage mechanics and added to the Cauchy stresses due to deformations.If the material remains linear-elastic,the proposed model reduces to the classical Rayleigh stiffness-proportional damping model.Other nonlinear behaviors of structural damping,such as the degradation of the damping force with damage evolutions and the(partial)restoring of damping due to the unilateral effect of concrete under cyclic loadings,can also be well predicted.With the HHT-α method and the proposed model,the dynamic nonlinear analysis of general structures can be transformed into the conventional quasi-static nonlinear one of undamped structures.Finally the proposed model is applied to the nonlinear analysis of Koyna concrete dam under earthquake motions.The predicted results agree fairly well with other investigators and the observed phenomena,demonstrating its validity and capability for the nonlinear analysis of concrete structures under dynamic loadings.