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This paper presents a generalization of the widely used approach of Orowan for calculating the roll pressure in flat rolling of homogeneous rigid perfectly strips on viscoplastic sheets. In contrast to the original approach, the approach for viscoplastic sheets requires the analysis of the velocity field since the model is rate dependent. The present paper employs the solution for plane strain compression of a viscoplastic block for finding the through thickness distribution of stress and velocity. Strain rate hardening is taken into account by means of the Herschel-Bulkley model.