The stress-free strain originated from local chemical composition and phase transformation can significantly alter the microstructures of materials; and then affect their properties. In this paper, we developed an analytical method to calculate stress-strain field due to the non-uniform stress-free strain in a spherically symmetrical particle. Applying the method to a lithium ion (Li-ion) battery electrode, the evolution of Li-ion concentration and strain field during the lithiation process is studied. Our studies reveal that the maximum strain in the electrode generally occurs on surface of sample, and is mainly dependent on the difference of Li-ion concentration of surface and of center in sample. Decreasing the difference of Li-ion concentration can efficiently decrease the maximum strain so that cracks of electrodes can been prevented. Our analytical results provide a useful guidance for practical applications of energy storage materials.