The steady motion of spheres representing particles inside tubes filled with different fluids has been investigated using both a finite-element and a finite-volume method. The rheology of the fluids has been modelled by the power-law able to describe the shear-thinning (pseudoplastic) behaviour of a series of polymer solutions. New results have been obtained for a series of tube/sphere diameter ratios in order to investigate the wall effects on the drag exerted by the fluid on the sphere. The results agree well with previous simulations for an unbounded medium (infinite diameter ratio). Experimental investigations have also been carried out and simulated, and the results compare favourably with the experiments. The present simulations revealed the convergence of the drag coefficient to a constant value independent of tube-to-sphere diameter ratio when the power-law index approaches zero.