Red blood cells (RBCs) generally deform to adopt a parachute-like, torpedo-like, or other configuration to align and flow through a capillary that is narrower than their major axis. As described herein, even in a narrow tube (25 microm) with diameter much larger than that of a capillary, flowing RBCs at 1 mm/s align axially and deform to a paraboloid shape in a viscous Newtonian fluid (505 kDa dextran medium) with viscosity of 23.4-57.1 mPa.s. A high-speed digital camera image showed that the silhouette of the tip of RBCs fits a parabola, unlike the shape of RBCs in capillaries, because of the longer distance of the RBC-free layer between the tube wall and the RBC surface ( approximately 8.8 microm). However, when RBCs are suspended in a "non-Newtonian" viscous fluid (liposome-40 kDa dextran medium) with a shear-thinning profile, they migrate toward the tube wall to avoid the axial lining, as "near-wall-excess," which is usually observed for platelets. This migration results from the presence of flocculated liposomes at the tube center. In contrast, such near-wall excess was not observed when RBCs were suspended in a nearly Newtonian liposome-albumin medium. Such unusual flow patterns of RBCs would be explainable by the principle; a larger particle tends to flow near the centerline, and a small one tends to go to the wall to flow with least resistance. However, we visualized for the first time the complete axial aligning and near-wall excess of RBCs in the noncapillary size tube in some extreme conditions.