This paper describes a new roller die design capable of generating high pressures to allow the direct injection of liquid carbon dioxide into polymer melts and produce low density foams. The novelty of the design lies in the counter-flow action of a pair of rotating rollers separated by a gap to build up pressure. A mathematical model of the flow in the extrusion-roller die system is described and tested against experimental data with PS, LDPE and PP under a wide range of roller speeds and gaps. The study shows that this new design is feasible but more comprehensive CFD simulations and experiments are required to optimise design and operation to obtain the low-density polymer foams sought.