This work focuses on the extrusion foaming under CO2 of commercial TPV and how the process influences the final morphology of the foam. Moreover, numerical modelling of the cell growth of the extrusion foaming is developed. The results show how a precise control on the saturation pressure, die geometry, temperature and nucleation can provide a homogeneous foam having a low density (<500 kg/m3). This work demonstrates that an optimum of CO2 content must be determined to control the coalescence phenomenon that appears for high levels of CO2. This is explained by longer residence times in the die (time of growth under confinement) and an early nucleation (expansion on the die destabilizes the polymer flow). Finally, this work proposes a model to predict the influence of CO2 on the flow (plasticizing effect) and a global model to simulate the extrusion process and foaming inside and outside the die. For well-chosen nucleation parameters, the model predicts the final mean radius of the cell foam as well as final foam density.