AbstractRock materials are often subjected to medium- and low-strain-rate dynamic cyclic loading such as earthquake action; however, few dynamic constitutive models for rock materials under dynamic cyclic loading are available. Therefore, it is important for evaluating the stability of rock engineering when analyzing the effects of seismic loading to establish a reasonable dynamic constitutive model for rock materials. This model can simulate the main characteristics of rock materials, such as the hysteresis loop, cumulative plastic deformation, strain rate effect, and damage effect. Thus, the formulation of a new dynamic constitutive model able to reproduce the cyclic behavior and dynamic mechanical properties of rock materials under dynamic cyclic loading is demonstrated and validated. First, by analyzing the variation of Young’s modulus for different rock materials under static and dynamic cyclic loading, it is assumed that there exist strain rate effect and damage effect on the Young’s modulus of rocks when subjected to dynamic cyclic loading. The expression of Young’s modulus for rock materials suitable for medium- and low-strain-rate dynamic cyclic loading is established. Second, like the variation of Young’s modulus, the expressions of cohesion and internal friction angle with strain rate and damage variable for rock materials under dynamic cyclic loading are also established. Then, a dynamic constitutive model for rock materials considering strain rate, damage effect, and the coupling of the former two effects is constructed based on the static constitutive model proposed by a previous study. Finally, the dynamic and static constitutive models are applied to simulate the behavior of a T2y6 marble and a material similar to basalt under uniaxial constant amplitude dynamic cyclic loading and triaxial damage-controlled cyclic dynamic loading (using increasing mean and amplitude stress). The results show that the results obtained by the proposed model, in terms of reproducing the compressive strength, Young’s modulus, and residual strain in cyclic tests of the two rock materials, are much better than those predicted by the static constitutive model.