Polymer solutions flowing through small-diameter capillaries of which length scale is much larger than that of polymers were experimentally demonstrated to have the enhanced flow rate as compared to in bulk flow. This apparent slip phenomenon was analyzed by obtaining the slip velocity and concentration depleted layer thickness. Hydrolyzed polyacrylamide (HPAM) of highly flexible polymer and Xanthan of rigid rodlike polymer were made to flow through stainless steel capillaries having the diameter range of about 100 to 250 mum. The results showed that both slip velocity and depleted layer thickness decreased markedly with increasing polymer concentration. This behavior can be interpreted as being due to the reduction of diffusion coefficient and flexibility of polymer chains as the concentration is increased. The depleted layer thickness of HPAM was much larger than the polymeric length scale and was shown to increase with increasing wall shear stress. This is considered as an evidence of the stress-induced diffusion of polymer chains being a dominant factor for the apparent slip of flexible polymer solution. On the other hand, the depleted layer thickness of Xanthan solution was almost constant with the wall shear stress, which can not be explained by the stress-induced diffusion mechanism alone.