Coating of a precursor structure, which is subsequently removed by chemical or thermal treatment, is a technology for producing cellular materials with interesting properties, for example in the form of metallic sponges with hollow struts. In this paper idealized models for determining the effective elastic properties of such materials are presented. The chosen models for the structures are space-filling, periodically repeating unit cell models based on idealized models of wet foams, which were generated with the program ‘Surface Evolver’. The underlying topology is that of a Weaire-Phelan structure. The geometry of the micro-structures can be described by two principal parameters, viz. the volume fraction of solid material in the precursor structures, which determines the shape of the final structures, and the thickness of the metallic coating, which defines their apparent density. The influence of these two parameters on the macro-mechanical behavior is investigated. The elastic properties of the micro-structures are described by three independent elastic constants owing to overall cubic material symmetry. The dependence of the effective Young’s modulus on the direction of uniaxial loading is investigated, and the elastic anisotropy of the structures is evaluated.