Previous numerical simulations for the flow of Bingham plastics past a sphere contained in cylindrical tubes of different diameter ratios are extended to Herschel-Bulkley fluids with the purpose of comparing them with experiments. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient as a function of the pertinent dimensionless groups. Good overall agreement is obtained between the numerical results and the experimental studies. (C) 1997 Elsevier Science B.V.