The influence of friction conditions in the deformation cell is studied, taking into account the differences of the distribution of contact stresses on the drive and non-drive rolls, on the normal pressure and rolling force. The research methodology involved the development of a mathematical model of the process and conducting a numerical experiment. The rolling process model is based on the numerical solution of the Karman`s equation using the Coulomb friction law and boundary conditions appropriate of the rolling process with a single drive roll. When conducting a numerical experiment, the coefficient of friction in the deformation cell was changed at four levels in the range from 0.15 to 0.30. The coefficient of friction in the journal bearings non-drive rolls was varied at three levels. From the analysis of the obtained distributions of contact stresses along the length of the deformation cell by the drive and non-drive rolls, it was found that with decreasing the coefficient of friction in the deformation cell, the normal pressure decreases proportionally, as well as the difference between the pressure on the drive and non-drive rolls. The occurrence of longitudinal tensile stresses with a coefficient of friction in the deformation cell of 0.25 and more is noted. The coefficient of friction in the non-drive roller bearings, for the entire range of values taken, does not have a significant effect on the contact stresses, pressure and rolling power. The presence of tensile stresses when rolling with one drive roll leads to a decrease in the average pressure and rolling power within 8-10%. Therefore, rolling with one drive roller can be used to reduce energy costs. In addition, the presence of tensile stresses, at certain values of the coefficient of friction in the deformation cell, accordingly affects the mechanical and technological properties of the rolled products, but this feature of the process requires additional study.