A rate-dependent model for the plane-strain sheet-rolling problem is proposed. The governing equations are solved using an asymptotic scheme that assumes that the ratio δ of thickness of the sheet material at the entry to the roll-bite length is small. Both the relative-slip and no-slip sheet-roll interface conditions are considered. Depending on the magnitude of the friction, different regimes that correspond to different levels of shear deformation have been identified and asymptotic solutions are provided for each of these regimes. The effect of the reduction, the strain-rate hardening parameter and the magnitude of the friction on the field variables and the roll-speed is also studied. Further, it is shown that in the limit as the strain-rate hardening index n -> ~, the asymptotic solutions for the rate-dependent model are shown to approach those predicted by rigid perfectly-plastic theory. The theoretical predictions are compared with experimental results for a commercial purity aluminum. The comparisons indicate a reasonable agreement between theory and experiment.