The mechanical behavior of cellular materials appears to have, for both open and closed cells, similar characteristics. The compressive stress-strain diagram contains a nearly elastic regime; this leads to a limit load, followed by a plateau extending to a strain of about 50% on average. All of the main features of this curve are related to the material's microstructure. In this study, taking into account the complex deformation mechanisms occurring in a cellular material under external loading, we introduced a statistical micromechanics model. The geometry of our analysis was based on a previous study, where the deformation of the individual struts was connected to the macroscopic deformation tensor. Assuming further that deformation was separated into elastic and viscoplastic parts and following a specific kinematic procedure, we simulated the compressive stress-strain response, the rate dependence, and the loading-unloading behavior of polymeric foam materials. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci 121: 3262-3268, 2011