Gradients in Li+ ion concentration distribution in a carbon fiber are accompanied by nonuniform 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. This phenomenon decreases the mechanical properties of fibers if used in structural batteries and reduces the charging properties of the battery by initiating exfoliation of layers on the fiber surface. The radial crack propagation and possible damage evolution scenarios are analyzed using linear elastic fracture mechanics.