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The compressive behavior of lithium-iron phosphate battery cells is investigated by conducting in-plane constrained compression tests and out-of-plane compression tests of representative volume element (RVE) specimens. The results for cell RVE specimens under in-plane constrained compression tests without pre-strains and with pre-strains in the out-of-plane direction indicate that the load carrying capacity is characterized by the buckling of cell specimens. As the pre-strain increases, the nominal compressive stress-strain curve becomes higher. The nominal stress-strain curves in the out-of-plane direction were also obtained and used to determine the elastic moduli for the elastic buckling analyses of the cell components in the cell RVE specimens with different pre-strains. Based on the elastic buckling analyses for a beam with different lateral constraints due to different pre-strains in the out-of-plane direction, the number of half waves and the buckling stresses were obtained.