A lattice-Boltzmann method has been developed to simulate suspensions of bo
th spherical and non-spherical particles in finite-Reynolds-number flows. T
he results for sedimentation of a single elliptical particle are shown to b
e in excellent agreement with the results of Huang, Hu & Joseph (1998) who
used a finite-element method. Sedimentation of two-dimensional circular and
rectangular particles in a two-dimensional channel and three-dimensional s
pherical particles in a tube with square cross-section is simulated. Comput
ational results are consistent with experimentally observed phenomena, such
as drafting, kissing and tumbling.