Row through an inclined tube of a suspension of uniform, neutrally buoyant spheres in a second-order fluid has been analyzed using the theory of (Li and Slattery, 1989). The result predicts that the spheres will migrate toward the center of the tube, forming a core with a maximum packing density. The velocity and concentration distributions agree qualitatively with previous observations. The predicted apparent viscosity is significantly lower than that obtained with a cone-plate viscometer (limiting case in which the angle between the cone and the plate approaches zero), or a parallel-plate viscometer, in which uniform concentration distributions are expected.