The separator is a critical component to the durability and safety of a battery. In a Li-ion battery, the dimensional change of the electrodes due to Li insertion/removal and the thermal expansion mismatch between components may induce stresses in the separator. Currently, there is no method to evaluate the stress inside a battery. This paper presents a finite element based multi-scale approach for the stress analysis of the separator in a battery cell. In this approach, the stress and deformation due to Li intercalation in electrode particles and separators is computed with a meso-scale representative volume element (RVE) battery cell sub-model coupled to a 1D macroscopic battery in the multi-physics code COMSOL®. A LiC6/LiPF6/Li y Mn2O4 battery cell is analyzed. As the first step, only the effect of dimensional change due to Li insertion/removal is considered. The simulation results revealed that the stress in the separator vary in phase with the battery cycles. Its state and magnitude depended upon the Young's modulus of the separator, electrode particle size, packing, and the pressure of the cell. The results also suggested that the net cyclic dimensional variation of the battery cell accompanied with Li insertion/removal can be controlled by battery design.