The effect of stress on storage particles within a lithium-ion battery, while acknowledged, is not fully understood. In this study we identify the importance of solid mechanics in the performance and reliability of the system. We identify three non-dimensional parameters that govern the stress response within a spherical storage particle, and we describe the results of numerical simulations that characterize particle stresses. The non-dimensional groups contain system parameters such as the diffusion coefficient, the particle radius, the lithium partial molar volume and the host material's Young's modulus. Stress maps are presented for various values of these parameters for fixed rates of insertion and extraction, with boundary conditions applied to particles similar to those found in a battery. Stress and lithium concentration profiles for various values of these parameters show that the coupling between stress and concentration is magnified depending on the values of the parameters.