The Lattice-Boltzmann method (LBM) is used for the computation of the total hydrodynamic force acting on a solid sphere that settles in a viscous fluid contained in orthogonal cylindrical or prismatic enclosures. Creeping flow as well as flows with finite Reynolds numbers are computed. Among the several geometrical flow domains that are examined are: a sphere in an orthogonal circular cylinder and a sphere in a prismatic enclosure with various rectangular cross-sections. We also performed calculations on the flow and the hydrodynamic force developed on the sphere, when it does not move along the line of symmetry of the enclosure. In the last type of calculations, we have found out that a transverse component of the hydrodynamic force develops. In the absence of any rotation of the sphere and for the range of Reynolds numbers examined here, this force is directed towards the axis of symmetry of the enclosure. (C) 2002 Elsevier Science Ltd. All rights reserved.