Cellular rubbers are elastomeric materials containing pores which can undergo large volumetric deformations. This contribution presents an isotropic, hyperelastic material model for cellular rubbers based on the approach of Danielsson, Parks, & Boyce (2004). For model validation and parameter fitting, experimental characterization were carried out for a foamed elastomers based on a natural rubber compound. Moreover, a feasible procedure of parameter fitting avoiding lateral strain measurement is outlined and tested. Furthermore, a finite element model of the microstructure of the cellular rubber is reconstructed from a computer tomography scan.