The present study analyses the influence of a viscoelastic sheet of finite initial thickness on the calendering process. The rheological constitutive equations of the fluid under consideration follows the Simplified–Phan–Thien–Tanner (SPTT) fluid model. The corresponding governing equations of mass and momentum balance, based on lubrication theory, are solved numerically, obtaining quantities of fundamental interest such as the pressure gradient, pressure distribution, and velocity profiles, once the above variables were obtained, the dimensionless leave-off distance in the calendering process was determined. Our results show that the inclusion of a viscoelastic material at the calendering process substantially modifies all these dimensionless variables in comparison with those developed under a Newtonian context.