A theoretical model was developed to describe the calendering process in viscoelastic sheets of finite initial thickness. The rheological constitutive equation of the fluid under consideration follows a common form of the Simplified-Phan-Thien-Tanner (SPTT) fluid model. We predict the influence of the viscoelastic effects on the leave-off distance that is related to the exiting sheet thickness in the calendering process. The mass and momentum balance equations, which are based on lubrication theory, were non-dimensionalized and solved for the velocity and pressure fields by using perturbation and numerical techniques, where the leave-off distance represents an eigenvalue of the mathematical problem. When the above variables were obtained, the dimensionless leave-off distance in the calendering process was determined, considering the influence of the viscoelastic effects in the process. Moreover, quantities of engineering interest were calculated, including the maximum pressure, the roll-separating force and the power transmitted to the fluid by the rolls. The results show that the inclusion of the viscoelastic effect substantially modifies all dimensionless variables in comparison with those obtained for the Newtonian case. (C) Elsevier B.V. All rights reserved.