Velocity, pressure, temperature, and stress fields are calculated for the flow of a polymer between two counterdirectionally rotating rolls. The rheological behavior of the polymer is described by the Carreau equation, while elasticity is neglected. The results of the numerical calculations are compared with measurements. The stress field is measured by the birefringence method. The local principal stresses in the fluid are determined from the measured anisotropy of the sheared fluid for the penetrating monochromatic light by means of the stress optical law. The equations of motion and continuity are solved with a Finite Element Method (FEM) based on the Galerkin weighted residual method. The computer code is combined with a Boundary Element Method (BEM) algorithm using the Dual Reciprocity Method (DRM) to solve the coupled equation of energy. Results are shown for a shear-thinning polyisobutene melt in a calender with totally submerged rolls. The calculated results for the principal stress differences are compared to the measured results and confirm fairly well. The influence of friction is discussed.