An analytical model of mechanical contact problems in composite electrodes of lithium-ion batteries is developed in this article. Two typical types of mechanical contact, namely contact between particles and contact between particle and current collector, are investigated. Key parameters that affect the contact problem are identified from the analytical solution. High uniformity of the particle size is found to be critical to the electrode. Furthermore, a soft current collector could significantly reduce the contact stress and hence is also suggested. It is figured out that contact stress is comparable to or even higher than the diffusion-induced stress under free-expansion state, even if the mechanical constraint in electrodes is weak. To highlight the significance of contact stress, an electrochemical cycling verification experiment which involves a charging pause is conducted. Both analytical and experimental results indicate that the mechanical contact plays a crucial role in the evaluation of mechanical stability of lithium-ion battery electrodes.