From the summary: We develop a finite element model of large deformation, plane strain rolling contact between rubber-coated rolls with thin media in the nip. The rubber layers on each roll are modeled as incompressible hyperelastic neo-Hookean materials. Steady rolling contact is analyzed using a standard Lagrangian finite element code with a modified friction algorithm, which converts the code from a Lagrangian framework to an Eulerian framework. The case of a rigid roll against a layered roll is also presented. Numerical results illustrate the effects of indentation, nominal speed ratio and paper velocity and traction distributions in the nip.