This paper develops a multi-scale mechanical-electrochemical model which enables fully coupled mechanics and electrochemistry at both particle and electrode levels. At the particle level, solid diffusion is modeled using a generalized chemical potential to capture the effects of mechanical stress and phase transformation. At the electrode level, the stress arising from particle interaction is incorporated in a continuum model. This particle interaction stress is in addition to the traditional concept of intercalation stress inside isolated particles. The particle and continuum electrode levels are linked by the particle interaction stress as loads on the particle surface, and by consideration of stress on the electrochemical reaction rate on the particle surface. The effect of mechanical stress on electrochemical reaction results in a stress-dependent over-potential between particle and electrolyte. Stress gradient in an electrode leads to inhomogeneous intercalation/deintercalation currents for particles depending on their interaction stress with neighbors, resulting in stress gradient induced inhomogeneous state of charge. Conversely, non-uniform intercalation/deintercalation currents in an electrode lead to stress between particles. With this model we have an important finding: an electrochemically inactive region in an electrode causes stress built-up. This model provides a powerful tool to address various problems such as fracture in-between particles.