A focus on the basic science on batteries is on modeling existing and emerging battery characterization techniques, such as Electrochemical Strain Microscopy (ESM). Here, numerical techniques are being developed to demonstrate the effect of the relevant transport paths within polycrystalline thin film and the extent of lithium diffusion into the electrode as a function of the ESM-tip-imposed overpotential frequency. Recent results demonstrate that the crystallographic orientation of electrochemically-actuated grains has a significant impact on the entirety of the intercalation process, including effective stored charge, discharge rate, electrochemically induced stresses, and side reactions. Simulations also demonstrate that continuous battery cycling results in a cumulative capacity loss as a result of successive non-reversible lithium intercalation. Results also demonstrate that ESM has the capability of inferring the local out-of-plane lithium diffusivity and the out-of-plane contributions to Vegard’s tensor