Soft rubber foams like poly(ethylene-co-vinyl acetate) (EVA) are industrially applied in a broad range of products, including sports gear, insulation materials and drug delivery systems. In contrast to glassy polymers, few studies in literature concern the foaming of soft rubbers using supercritical carbon dioxide. In this study, open microporous matrices of EVA have been formed with CO2. Prior to the foam expansion, sorption and swelling isotherms of CO2 in EVA have been measured and the obtained isotherms have been correlated using the Sanchez–Lacombe equation of state. Additionally, a pressure-independent diffusion coefficient of CO2 in EVA has been obtained from these experiments. The microporous foams have been formed by a pressure quench of the CO2-swollen polymer matrix. Sorption pressure as well as temperature and decompression times appear to determine the pore size and bulk density of the foam. These parameters allow for a control of the foam structure of EVA rubbers.