During cycling, mechanical stresses can occur in the composite electrode, inside the active material, but also in the solid electrolyte interphase layer. A mechanical model is proposed based on a system made of a spherical graphite particle surrounded by the solid electrolyte interphase layer. During lithium intercalation or de-intercalation, stresses in the graphite are produced, governed by the diffusion induced stress phenomena and in the solid electrolyte interphase, driven by the graphite expansion. The stresses in both materials were simulated and a sensitivity analysis was performed to clarify the influence of principal parameters on both processes. Finally, assuming that the solid electrolyte interphase is the weakest material and therefore more prone to fracture than graphite, the experimental capacity fade during cycling was modeled based on its break and repair effect rather than on the fracture of the active material. The mechanical model of the solid electrolyte interphase was implemented in a single particle lithium ion battery model in order to reproduce capacity fade during battery lifetime. The model results were compared against cycle life aging experimental data, reproducing accurately the influence of the depth of discharge as well as the average state of charge on the capacity fade.