Summary: The low density related to the high strength of the structure, and the special features of metal foams make it possible to develop special components. To design the properties of such components, the finite element method offers a cheap possibility for simulations. This requires the development of a model for foamed materials. In contrast to a microscopic approach, the theory of porous media allows a macroscopic continuum mechanical description for metal foams on the basis of a real or virtual homogenization over the microstructure. In particular, here we consider a gas-filled solid material taking into account finite elastic and finite elasto-plastic constitutive equations for the solid matrix combined with convenient constitutive relations for viscous pore-fluid and with the respective interaction mechanisms between the constituents.