Recently a new phenomenon of bonding polymeric films in solid-state, via symmetric rolling, at ambient temperatures (≈20 °C) well below the glass transition temperature (Tg≈78°C) of the polymer has been reported. In this new type of bonding, polymer films are subject to plane strain active bulk plastic compression between the rollers during deformation. Here, we analyze these plane strain cold rolling processes, at large strains but slow strain rates, by finite element modeling. We find that at low temperatures, slow strain rates, and moderate thickness reductions during rolling (at which the Bauschinger effect can be neglected for the particular class of polymeric films studied here), the task of material modeling is greatly simplified and enables us to deploy a computationally efficient, yet accurate, finite deformation rate-independent elastic–plastic material behavior (with the inclusion of isotropic-hardening). The finite deformation elastic–plastic material behavior based on (i) the additive decomposition of stretching tensor ( D = De+Dp, i.e., a hypoelastic formulation) with incrementally objective time integration and, (ii) multiplicative decomposition of deformation gradient (F=FeFp) into elastic and plastic parts, are programmed and carried out for cold rolling within Abaqus Explicit. Frictional interactions are modeled using a consistent rate-independent Coulombic law. Predictions from both formulations, i.e., hypoelastic and multiplicative decomposition, closely match the experimentally observed rolling loads. No specialized hyperelastic/visco-plastic material model is required to describe the behavior of the particular blend of polymeric films under the conditions described here, thereby significantly speeding up the computation for steady-state rolling simulations. It is revealed that under the deformation conditions when principal axes show negligible rotation, hypoelastic formulation can be valid at large elastic stretches. Moreover, the use of classical rigid-plastic modeling (often applicable to metals) is found to greatly underestimate the rolling loads for polymers due to large elastic stretches in the polymer films at large strains. Deformation aspects of solid-state polymeric sheets presented here are expected to facilitate the development of new processes involving (or related to) cold roll-bonding of polymers.