One of the critical challenges in advancing lithium ion battery performance is increasing mechanical stability of the solid electrolyte interphase (SEI) layers. Our work aims at developing a mathematical model to study the lithium ion concentration and stress in the SEI on the graphite anode. The main influence factors on the SEI stress have been thoroughly investigated. We find that the ion transportation of the SEI has the underlying effects on the maximum stress in the graphite active layer, especially at a high charging rate. The physical properties of the SEI should be taken into account to obtain an accurate anode stress. The tensile SEI stress along the hoop direction is dominant, and should be regarded as the leading cause of mechanical failure for the SEI. Moreover, the peak stress in the SEI is independent of the charging rate, but can be effectively reduced by rationally designing geometric and material properties of anode components by: (1) decreasing modulus of the SEI itself; (2) enhancing tensile stiffness of the current collector; and (3) making the ratio of anode radius to thickness larger than ten.