Solid electrolyte interphase (SEI) is known to be heterogeneous which comprises inorganic and organic decomposition products. To assess the effects of heterogeneity on the stability of the SEI, we establish a mathematical model in simulating the stress of heterogeneous SEI. Comparing with the analytical solution of stress in the homogeneous film, the heterogeneity of SEI is identified to be essential in the stress calculation of the inorganic layer, which is proven decisive for the stability of SEI. Further, the peak tensile stress within the inorganic layer is found in the bilayer SEI. It generates at the interface between the active material and the inorganic layer when the battery is fully charged. In addition, the impacts of the interface parameter, modulus, Poisson's ratio, thickness of SEI and lithiation properties of active material on SEI stress are systematically investigated. Based on the simulation results, this work provides insights into the stress analysis of the heterogeneous SEI, as well as suggestions in pursuing a well-designed SEI, i.e., a functional gradient heterogeneous SEI in which the inner layer close to the active material provides sufficient mechanical performance while the outer layer near the electrolyte performs good chemical and electrochemical behaviors, to enhance the battery performance.