Maxwellian fluid flow between asymmetric calenders was analyzed by the numerical solution to the simplified equations of motion and energy equation. The solution techniques combined the power-law weighted upwind difference method for the energy equation with the analytical solution of the momentum equations. The calculated results provided not only pressure and temperature distributions of the flow field, but also the power consumption and the roll separating force of the calendering processes. The decrease in the elastic shear modulus led to the reduction in the temperature profile as well as in the power requirement. The asymmetry in the roll speeds generated higher temperature field throughout the whole flow region due to the higher viscous heating, compared with the case of the symmetry in the roll speeds.