An ensemble of Hookean dumbbells is used to predict the material functions of a dilute polymer solution in simple shear and pressure‐driven channel flow. Attention is paid to the symmetries of the functions, which are approximated via the Galerkin method, using a complete set of trigonometric bases. The stress tensor exhibits a spatial variation which is the result of steric hindrance of the dumbbells by the confining walls. The apparent slip velocity for simple shear and pressure‐driven flow demonstrates that the steric hindrance hypothesis can reconcile anomalous enhanced volumetric flow rates with theory for channels no larger than one order of magnitude greater in size than the root mean square (rms) extension of the macromolecules.