AbstractThe viscoelastic damping materials (VDMs) used in the viscoelastic (VE) damping equipment may undergo thermal-oxidative aging during long-time exposure to complicated working environments and exhibit significant property degradation in their lifespan. Therefore, it is imperative to comprehend the mechanical performance of VDMs after aging. In this paper, the molecular chains of VDMs are categorized into elastic chains and free chains, and the effects of variable physical–chemical reactions in the thermal-oxidative aging process on these two kinds of chains are analyzed and then mathematically described based on the theory of chemical kinetics. By introducing the molecular chain statistical model to consider the influence of microstructure change on the macroscopic mechanical behavior of VDMs, a hyperelastic hybrid molecular chain model for thermal-oxidative aging VDMs is addressed in conjunction with the tube constraint model and filler reinforcement theory. Combined with the test data, the accuracy and applicability of the proposed model are comparatively evaluated, and the sensitivity analyses on the mechanical parameters and aging parameters of the proposed model are also conducted. The verified results suggest that the proposed model can reflect the mechanical behavior of aging VDMs during thermal-oxidative conditions with remarked accuracy. The results of the parameters analyses display that the macroscopic mechanical property of VDMs is prominently affected by their macromolecular chain structure, and the physical–chemical reactions occurring in the aging process synthetically play a collaborative influence on the mechanical performance of aging VDMs.