In this investigation, the study of a non-Newtonian material when it is dragged through the narrow region between two corotating rolls is carried out. Theoretical analysis based on the lubrication approximation theory (LAT) shows that LAT is a good predictive tool for calendering, where the sheet thickness is very small compared with the roll size. By considering the influence of the material parameter, the dimensionless leave-off distance in the calendering process is determined. The leave-off distance is expressed in terms of eigenvalue problem. Quantities of engineering interest like the maximum pressure, the roll-separating force, the power transmitted to the fluid by rolls, and the normal stress effect are calculated. It is observed that the material parameter has great influence on detachment point, velocity, and pressure distribution, which are useful for the calendering process.