The interactions of two identical rigid spheres of radius R translating in a Bingham material in creeping flow along their line of centers are calculated at various sphere separations using the finite element method. The yield surfaces are determined by an extrapolation using a regularized constitutive model. Two spheres falling in a line interact at separations greater than that corresponding to the superposition of yield surfaces for isolated spheres falling in an unbounded medium. Three distinct regimes are identified: for L / R > 5.5, the spheres move in separate yield envelopes; for 4 < L/R < 5.5, the spheres fall in a single coalesced envelope in which at least part of the region between the spheres is yielded; for L/R < 4 the spheres fall in a coalesced envelope and are connected by an unyielded plug. Drag reduction of up to 30% relative to the single-sphere case is observed as the sphere separation is decreased. The yield surfaces for two approaching spheres show a shorter range of interaction compared to the case of two falling spheres; a very slight drag reduction relative to the single-sphere case is observed for two approaching spheres. (C) 2003 Elsevier B.V. All rights reserved.