During the charging and discharging process of a lithium-ion power battery, the intercalation and deintercalation of lithium-ion can cause volume change in the jellyroll and internal stress change in batteries as well, which may lead to battery failures and safety issues. A mathematical model based on a plane strain hypothesis was established to predict stresses in both the radial and hoop directions, with the hoop stress of each winding layer of the jellyroll obtained. Displacements of the steel case, the jellyroll, and the core of the battery during the charging and discharging processes were also analyzed, with the effect of lithium-ion concentration and the battery size discussed. The research results can explain well the wrinkling and fracture of the jellyroll.