Heterostructured nanowires are of prime interest in nowadays technology such as field-effect transistors, field emitters, batteries and solar cells. We consider their aging behavior and developed a model focusing on reactive diffusion in core-shell nanowires. A complete set of analytical equations is presented that takes into account thermodynamic driving forces, vacancy distribution, elastic stress and its plastic relaxation. This complete description of the reactive diffusion can be used in finite element simulations to investigate diffusion processes in various geometries. In order to show clearly the interplay between the cylindrical geometry, the reactive diffusion and the stresses developing in the nanowire, we investigate the formation of an intermetallic reaction product in various core-shell geometries. Emphasis is placed on showing how it is possible to control the kinetics of the reaction by applying an axial stress to the nanowires.