Lithium-ion batteries (LIBs) are widely used in energy storage owing to their high energy density and long cycle life, but battery aging, especially capacity fade associated with the formation and growth of the solid electrolyte interphase (SEI) film on the anode, limits service life and cycling performance. Although many efforts have been made to the modeling of SEI chemistry and transport, the mechano-chemical coupling between stress evolution and SEI film growth-induced capacity loss in silicon-based anodes remains unclear. Building on the classical Doyle-Fuller-Newman cell model, we describe diffusion-limited SEI film growth and introduce a local hydrostatic stress term into the overpotential of the SEI-forming side reaction, thereby obtaining a stress-coupled kinetic equation for the side-reaction current density. This framework captures how lithiation-induced particle expansion generates hydrostatic stress, how this stress modifies electrolyte-reduction kinetics, and how the resulting SEI film thickening feeds back to influence further stress evolution. Simulations show that hydrostatic stress exponentially amplifies the side-reaction current density, accelerates SEI film accumulation, and thereby intensifies capacity fade, while neglecting stress coupling underestimates the SEI film growth rate and degradation severity. Parametric studies reveal that, within a non-cracking regime, increasing the silicon particle radius reduces the normalized SEI film thickness and improves capacity retention, whereas decreasing the depth of discharge shortens the time window for side reactions, suppresses SEI film growth, and mitigates degradation. By establishing this mechano-chemical framework, the study clarifies the link between SEI film growth and capacity loss and provides theoretical support for lifetime prediction and failure mitigation in next-generation high-energy-density LIBs.