The boundary effect on the drag acting on a rigid particle is investigated by considering a spheroid on the axis of a cylinder filled with a Carreau fluid. The result of numerical simulation reveals that the ratio (drag coefficient in Carreau fluid/drag coefficient in Newtonian fluid) has a maximum as the ratio (semiaxis in radial direction/radius of cylinder) varies. The presence of a wall has the effect of enhancing the convective motion in the rear part of a particle, and therefore, the formation of wakes. The influence of the shape of a particle on the drag force acting on it can be decreased either by increasing the shear-thinning effect of the fluid or by increasing the Reynolds number. The Reynolds number at which flow separation occurs is found to increase roughly linearly with the increase in the power-law exponent of the Carreau fluid.