Microcellular polystyrene foams have been prepared using supercritical carbon dioxide as the foaming agent. The cellular structures resulting from this process have been shown to have a significant effect on the corresponding mechanical properties of the foams. Compression tests were performed on highly expanded foams having oriented, anisotropic cells. For these materials an anisotropic foam model can be used to predict the effect of cell size and shape on the compressive yield stress. Beyond yield, the foams deformed heterogeneously under a constant stress. Microstructural investigations of the heterogeneous deformation indicate that the dominant mechanisms are progressive microcellular collapse followed by foam densification. The phenomenon is compared to the development of a stable neck commonly observed in polymers subjected to uniaxial tension, and a model that describes the densification process is formulated from simple energy balance considerations.