While different subtopics of degradation of rubber under strain, temperature, wear, tire-road abrasion or fatigue are discussed in detail from an experimental and numerical point of view in other chapters, this chapter mainly aims at the numerical aspects of the model setup from the material to the structural scale. The objective of this chapter is to establish the link between experimental testing on the material scale and predictive simulation on the structural scale. To demonstrate the general procedure in the context of the finite element method (FEM), thermal damage or thermal aging as one phenomenon of material alteration over time is addressed by developing a corresponding continuum mechanical model. The phenomenological model is derived at the material scale and integrated at the structural scale by solving the thermo-mechanically coupled problem for the example of a rubber-cord structure in the form of an automobile tire. With the structural model at hand, simulations of the entire lifetime become feasible. Future trends in this context are introduced by focusing on the further extension of the pure simulative approach to cyber-physical systems (CPS), e.g. for the holistic assessment of the impact of tire wear particles (TWP) on the environment (definition of system boundaries, material flows, and interactions).