The majority of rubbery components in industrial applications is subject to environmental influences. Especially exposition to oxygen leads to changes in the material behaviour due to reaction of the network structure with oxygen. The speed of these reactions depends on the availability of oxygen which is determined by a diffusion process. To enable realistic simulations of the oxidative ageing of such components, a coupled problem has to be solved. Furthermore, the resulting mechanical behavior is influenced by changes in stiffness as well as in commonly observed effects, e.g. softening, hysteresis and relaxation. Modelling these realistically is key to predict the change of important component features like dynamic stiffness and damping behaviour. A suitable hyperelastic chemo-mechanical model and an according solution strategy for the coupled problem were presented in previous publications. In order to predict a broader variety of aspects concerning the mechanical behaviour of oxidatively aged elastomers, a more sophisticated mechanical model has to be utilized. An existing constitutive model is investigated for its ability to describe the mechanical behaviour of an industrial compound for various ageing conditions. The model is then extended to include the effects of oxidative ageing. Measurements are presented for the quasi-static and the relaxation behaviour of the investigated natural rubber compound for various ageing conditions, including different ageing temperatures and ageing durations. A parameter adaption for the introduced model is shown to deliver realistic predictions for the mechanical behaviour of the aged material for all presented ageing conditions.