The present work deals with the development of a direct simulation strategy for solving the motion of spherical particles in a Bingham liquid. The simulating strategy is based on a lattice-Boltzmann flow solver and the dual-viscosity Bingham model. Validation of the strategy is first performed for single phase (lid-driven cavity flow) and then for two phase flows. Lid-driven cavity flow results illustrate the flow's response to an increase of the yield stress. We show how the settling velocity of a single sphere sedimenting in a Bingham liquid is influenced by the yield stress of the liquid. The hydrodynamic interactions between two spheres are studied at low and moderate Reynolds number. At low Reynolds number, two spheres settle with equal velocity. At moderate Reynolds number, the yield effects are softened and the trailing sphere approaches the leading sphere until collision occurs. (c) 2010 Elsevier Ltd. All rights reserved.