In this paper, computational models are developed for simulations of representative volume element (RVE) specimens of lithium-ion battery cells under in-plane constrained compression tests. For cell components in the finite element analyses, the effective compressive moduli are obtained from in-plane constrained compressive tests, the Poisson's ratios are based on the rule of mixture, and the stress–plastic strain curves are obtained from the tensile tests and the rule of mixture. The Gurson's material model is adopted to account for the effect of porosity in separator and electrode sheets. The computational results show that the computational models can be used to examine the micro buckling of the component sheets, the macro buckling of the cell RVE specimens, and the formation of the kinks and shear bands observed in experiments, and to simulate the load–displacement curves of the cell RVE specimens. The initial micro buckling mode of the cover sheets in general agrees with that of an approximate elastic buckling solution. Based on the computational models, the effects of the friction on the deformation pattern and void compaction are identified. Finally, the effects of the initial clearance and biaxial compression on the deformation patterns of the cell RVE specimens are demonstrated.