Variations of apparent viscosity with pore size in both the Newtonian and shear‐thinning regimes have been studied in noninertial flow of a rodlike polymer solution through well‐calibrated cylindrical pores, small glass bead beds, sharp‐edged particle packs, and a sandstone under conditions where flow properties are not influenced by polymeradsorption or retention. The bulk shear viscosities of microgel‐free xanthan solutions were accurately measured over a wide range of shear rates and polymer concentrations in order to determine macromolecular dimensions, confirm rodlike behavior, and know the effects of shear rate on intermolecular interactions. In fine pores, both the Newtonian apparent viscosity and the shear‐thinning index were found to decrease with pore size as long as pore diameters were larger than rod length. Such behavior is interpreted by the existence near the wall of a depleted layer in which steric hindrances decrease monomer concentration and thus viscosity near the wall. The proposed two‐fluid flow model satisfactorily predicts the experimental results in both cylindrical pores and stochastic porous media, confirming the dimensional origin of this depleted layer which is insensitive to both pore shape and the chemical nature of the wall.