Crumpled metal foils are a new type of lightweight cellular materials. The engineering applications of crumpled foils require a deep understanding of their response to mechanical loads. In order to establish a comprehensive understanding of the mechanical behavior of crumpled foils, in the present study, the uniaxial compression experiments were performed on cylindrical samples of different packing densities manufactured by die compaction of randomly crumpled aluminum foils. This has allowed us to deduce the constitutive stress-strain relationship and quantify the relaxation behavior of crumpled foils. Consequently, we determine the mechanical properties (apparent Young modulus, yield stress, and longitudinal stiffness modulus) that govern the deformation behavior of crumpled samples in the whole range of relative deformation. The power-law dependence of mechanical properties on the initial packing density is revealed. The stress and strain relaxation behavior of crumpled foils is also elucidated. These findings provide further insight into the deformation behavior and relaxation mechanisms of crumpled aluminum foils. The knowledge of the mechanical and relaxation characteristics of crumpled aluminum foils is useful for their engineering application.