The flow behavior of aqueous and organic polymer solutions in laminar flow was studied experimentally in small‐diameter tubes. The tube diameters ranged from 0.0190 to 0.1097 cm and theL/D(length/diameter) ratios were 20–2700. The experimental flow rates were abnormally higher than the predictions based on viscometric cone‐and‐plate data. This abnormal flow enhancement is termed hereapparent slipand it was quantified by an effective slip velocity. The effective slip velocity was found to increase with the wall shear stress. The contribution of slip, however, to the total flow rate for a given tube diameter decreased with increasing wall stress due to shear thinning. Additionally, for a given wall stress, the contribution of slip increased with decreasing tube diameter. Qualitatively, theapparent slipphenomenon is expected to occur for the flow of elastic high‐molecular‐weight, nondilute polymer solutions in inhomogeneous stress fields.