The influence of a contact surface shape of the deformation zone during cold rolling of a band on the rolling force subject to parameters of the strain strengthening curve of billet material and band tension has been studied by numerical methods. The comparison of the obtained results and well-known ones allowed one to set that in case of the presense of strain strengthening, the replacement of the arc of contact by the chord resulted in a decrease in calculated force of rolling, whose value depends on the presence of the fore tension and the back tension and parameters of strain strengthening of metal.