Numerical simulations have been undertaken for the process of calendering viscoplastic sheets with a finite thickness. The finite element method (FEM) is used to provide numerical results for a fixed entry thickness (known attachment point) under two-dimensional steady-state conditions. The Herschel-Bulkley-Papanastasiou model of viscoplasticity is used, which is valid for all ranges of deformation rates. Part of the solution is finding the shape of the free surfaces of the entering and exiting sheet. Yielded/unyielded regions are found a posteriori for a range of the dimensionless yield stress or Bingham number (Bn) from the Newtonian viscous fluid (Bn = 0) to a highly viscoplastic one (Bn = 1000). The 2D FEM results show limited unyielded regions between the rolls, in disagreement with the lubrication approximation theory (LAT). which predicts erroneous extended unyielded regions. However, LAT is good at predicting the excess sheet thickness over the thickness at the nip (hence the detachment point), the pressure distribution and all engineering quantities of interest in calendering. For thick entering sheets, viscoplasticity (and also shear-thinning) leads to excess sheet thickness as the dimensionless Bingham number increases; it reduces the vortex size in the fluid bank, and gives virtually no swelling at the exit from the rolls. All engineering quantities, given in a dimensionless form, increase substantially with the departure from the Newtonian values. (C) 2008 Elsevier B.V. All rights reserved.