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Operation of a flat slot die with rollers for the extrusion foaming of polymers, which has been originally designed by Benkreira et al. (Int. Polym. Proc., 19, 111 (2004)), is considered. The rotation of rollers makes it possible to independently control shear rate inside the die, in the bubble nucleation zone, thus influencing the cell density. In experimental studies of low-density polyethylene foaming, the influence of the roller rotation speed on the cell density at variable isobutane and talc concentrations and die outlet area has been determined. Based on the fluctuational nucleation theory, a simple model is proposed for estimating the number density of supercritical nuclei formed at the nucleation stage and evaluating the cell density in the foam with allowance for bubble coalescence effects. POLYM. ENG. SCI., 54:96–109, 2014. © 2013 Society of Plastics Engineers