A nonlinear phenomenological constitutive model applicable to structural foams subjected to large deformations is proposed. The five-parameter model can fully capture the three fundamental features of stress-strain response, i.e., linearity, plasticity-like stress plateau, and densification phases, when subjected to compressive loads. Moreover, the parameters of the model can be systematically varied to capture the influence of initial density of foams that may be responsible for changes in yield stress and hardening-like or softening-like behavior under various confinement conditions. The model was successfully applied to capture the stress-strain response of two structural foams of different initial densities when subjected to uniaxial compression without lateral confinement and unixial compression under rigid confinement.