Abstract: It is very important to establish a constitutive model for the dynamic response of rubber structure. Dynamic testing of disc rubber samples was carried out by dynamic thermomechanical analysis (DMA), obtaining experimental data of rubber dynamic response. Based on the superposition property of WORKBENCH constitutive model, a hyperelastic-viscoelastic constitutive model was established, in which the superelastic model characterizes the large deformation of rubber and the viscoelastic model characterizes the hysteresis effect of the rubber. Using the empirical formula, the parameters of the hyperelastic model were identified, and using the relaxation curve obtained by the DMA experiment through the ANSYS viscoelastic parameter fitting channel, the viscoelastic model parameters were identified. Establishing the simulation model consistent with the experimental conditions, the error between experimental data and simulation data is small and within a reasonable range. The correctness of the established hyperelastic-viscoelastic constitutive model was verified. The response characteristics of the disc-shaped rubber specimen and the cubic rubber specimen under the cyclic torsional load and vertical load were obtained, respectively. The applicability of the constitutive model was also verified. The dynamic response characteristics of the cubic rubber specimens in the hyperelastic-viscoelastic constitutive model, linear bomb-viscoelastic constitutive model and single hyperelastic bomb constitutive model show that the constitutive model has the best response to the dynamic response of the rubber structure. It provides a reference for the selection of rubber constructive models in engineering practical problems.