Although LiFePO4 has advantageous properties for electrical energy storage, it can lose some of its charging capacity when cycled. It has been suggested that crack formation is the main cause of the capacity loss. We shall discuss a multi-physics computational model to investigate the possible causes of fracture in single LiFePO4 particles. The model combines the recently developed reaction-limited phase-field model for Li-ion intercalation with a phase-field model for brittle fracture. We use our numerical model to simulate single LiFePO4 cathode particles during galvanostatic discharging as well as under no charging. It was found that because of the phase transformation and two-phase coexistence of LiFePO4, cracks grow due to large stresses at coherent phase boundaries. Phase nucleation at particle side facets was also examined and we show that pre-cracks grow that follow the high stresses at the coherent interface during charging.