Numerical simulations have been undertaken for the creeping flow of a Bingham plastic past a sphere contained in a cylindrical tube. Different diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The emphasis is on determining the extent and shape of unyielded/yielded regions along with the drag coefficient for the whole range of Bingham numbers. The present results extend previous simulations for creeping flow of a sphere in an infinite medium and provide calculations of the Stokes drag coefficient in the case of wall effects.