Abstract: Research on the diffusion stress in carbon fibers has primarily focused on all-solid-state electrolyte structures, with limited attention to solid-liquid bicontinuous systems. Bicontinuous structures, with complex pore characteristics, are typically reconstructed via transmission electron microscopy and analyzed with finite element method. This method is time-consuming, and the data obtained are insufficient to support comprehensive numerical studies, so it is necessary to use computer simulations to generate pore structures. It is more effective to generate the bicontinuous structure based on the horizontal Gaussian random field theory. While for the analysis, Finite Cell Method based on the idea of immersed boundary approach is an ideal candidate to deal with complex shaped models. Currently, Finite Cell Method is primarily focused on the elastic analysis of solids and their topology optimization problems, with limited application to diffusion-induced stress and mass transport in porous structures. Therefore, a diffusion stress model for energy storage structures is established using the Finite Cell Method and B-spline base functions. The boundary coupling terms of the current conservation equation are iteratively satisfied using Newton’s method. Besides, Wilson-θ method is used for the time integration of the diffusion equation, and the expressions of the conduction matrix, capacity matrix and the flux load vector are derived. In addition, the concentration induced initial strain field is treated as the body force, and a recursive formulation is derived to solve the electric potential and lithium concentration field. Finally, the diffusion stress field can be obtained. The diffusion stress in the carbon fiber of the energy storage structure using all-solid electrolyte is calculated. The calculation results are consistent with those of commercial finite element software. Based on Gaussian random field simulation, bicontinuous pore structures are generated, and the effects of pore size and porosity on the extreme value of diffusion stress are studied.