Mechanical behavior of lithium-ion battery modules is investigated by conducting tensile tests of the module components, constrained compression tests of dry module representative volume element (RVE) specimens, and a constrained punch test of a small-scale dry module specimen. The results of tensile tests of the module components are used to characterize the tensile behavior of module specimens. The results in-plane constrained compression tests of module RVE specimens indicate that the load carrying capacity is characterized by the buckling of the module components and the final densification of the module components, and the nominal stress-strain curves appear to be independent of the specimen height. The results of different compressive nominal stress-strain curves in the in-plane and out-of-plane directions indicate the module RVE specimens are anisotropic. The results of a buckling analysis of the module RVE specimens under in-plane constrained compression are in agreement with the experimental results. The module RVE specimen is dominated by the buckling of the aluminum heat dissipater sheet under in-plane constrained compression. Finally, the results of a constrained punch test of a module specimen are in agreement with those of the corresponding finite element analyses based on a macroscopic homogenized foam material model.