Our study is motivated by the need for development and deployment of reliable and efficient energy storage devices, such as lithium-ion batteries. However, the rate-capacity loss is the key obstacle faced by current lithium-ion battery technology, hindering many potential large-scale engineering applications, such as future transportation modalities, grid stabilization and storage systems for renewable energy. During electrochemical processes, diffusion-induced stress is an important factor causing electrode material capacity loss and failure. In this study, we present models that are capable for describing diffusion mechanisms and stress formation in LiFePO4 nanoparticles, a lithium-ion battery cathode material which promises an alternative, with the potential for reduced cost and improved safety. To evaluate mechanics of diffusion-induced fractures, a plate-like model is adopted with anisotropic materials properties and volume misfits during the phase transformation are considered. Stress distribution at phase boundaries and fracture mechanics information (energy release rates and stress intensity factors) are provided to further understand the stress development due to lithium-ion diffusion during discharging. This study contributes to the fundamental understanding of kinetics of materials in lithium-ion batteries, and results from our stress analysis provides better electrode materials design rules for future lithium-ion batteries.