The mechanical properties of foams render them valuable for applications requiring energy absorption under high-speed loading events. Plastic deformation in foam-like materials is not isochoric on a macroscopic scale. Consequently, the yielding in foams is assumed to be a function of the invariants J2 (deviatoric stress) as well as I1 (hydrostatic stress). The model for yielding criterion proposed by Deshpande and Fleck [1] captures, in particular, the characteristic behavior of foam-like materials like plastic collapse at nearly constant stress and steep rise in stress after densification. However, this model cannot be used if the macroscopic mechanical behavior of the foam is strain-rate dependent. This paper presents a viscoplastic constitutive model for foam-like materials building on the model proposed in [1]. Specifically, the viscoplastic flow rule developed by Peri ́c [2] is used to ac- count for strain rate effects. A non-linear isotropic hardening model is used to capture the macroscopic plastic response. The model is first tested using a material-point simulation in a one-dimensional setting. Subsequently, the three-dimensional constitutive equations are implemented in an explicit finite element solver. The parameters of the proposed viscoplastic model are determined based on experimental data available in the literature. A comparison of the performance of the proposed model with existing viscoplastic models will be presented. Detailed simulations exhibiting the utility of our viscoplastic model for foams will also be presented highlighting its ability to capture phenomena like strain rate dependence, creep, and stress relaxation. Further, preliminary results on the application of this model to understand the response of functionally graded foams under extreme loading conditions will be discussed. This model is expected to work for a wide range of strain rates (tested up to 500s−1) and is thus of interest in designing foams for high-strain rate applications.