Gradients in lithium ion concentration distribution in carbon fiber are accompanied by non-uniform fiber swelling leading to development of mechanical stresses. During lithium deintercalation these stresses may lead to initiation and growth of radial cracks in the fiber. The subsequent cycle of intercalation may result in arc-shaped cracks deviating from the tip of the radial cracks. These phenomena decrease the mechanical properties of fibers if used in structural batteries and reduce the charging properties of the battery by decreased diffusivity of lithium ions and by exfoliating layers on the fiber surface. The crack propagation and possible damage evolution scenarios are analyzed using linear elastic fracture mechanics. The crack geometry dependent ion concentration distributions and the elastic stress distributions were found using finite element software ANSYS.