The creeping flow of a Powell‐Eyring fluid through a sudden tubular contraction is considered, and finite difference solutions of the vorticity transport and stream function equations are obtained for a range of contraction ratios, fluid properties, and apparent shear rates. Calculated axial velocity profiles, excess pressure drops, and separation effects at the 90° corner of the contraction are compared with theoretical results for Newtonian fluids and with experimental data for polymer solutions and melts. The results indicate a strong influence of nonlinear viscous effects on the magnitude of the excess entrance pressure loss and on the extent of the circulation pattern at the corner of the contraction.