Part II of this study is concerned with the modeling of all aspects of the compressive response and crushing of the open-cell Al foam studied in Part I. The foam microstructure is modeled using the regular cell of Kelvin with cell anisotropy and ligament geometry established by X-ray tomography. The ligaments are modeled as shear-deformable beams and the material is elastoplastic calibrated to the properties of the Al alloy base material. It is demonstrated that the initiation stress of measured responses is associated with a limit load instability that results from plastification of foam ligaments due to combined bending and axial compression. The periodicity of the Kelvin cell enables calculation of the initial elastic properties as well as the initiation stress with just a single fully periodic characteristic cell. The crushing response is evaluated by considering finite size 3D domains that allow localized deformation to develop. Localization is in the form of shear buckling that develops along the principal diagonals of the Kelvin cell foam. Localized crushing is arrested by contact between the ligaments of the buckled cells. Contact is approximated by limiting the amount a cell can collapse in the direction of the applied load. This arrests local collapse and causes it to spread to neighboring material at a nearly constant stress level as in the experiments. The stress picks up when the whole domain has crushed. Although the calculated collapse patterns differed from the more random ones observed in the experiments, the calculated force-displacement responses match very well the experimental ones in all aspects.