The lift on a particle that is caused by its proximity to a boundary and the equilibrium position of this particle in a linear shear flow have been studied using the lattice Boltzmann method. The shear particle Reynolds numbers examined were in the range 0-18 and the particle to fluid density ratios were in the range 1.005-1.1. We have found that heavy particles will deposit at the bottom of the channel, while lighter particles remain suspended and attain an equilibrium vertical position, which is characterized by the equality of the lift and the gravity forces. At this equilibrium distance from the boundary, the vertical velocity component is zero, while the horizontal and rotational velocities of the particle are finite. For circular particles, we have found out that the equilibrium position is independent of the initial height of release of the particles and depends only on the density ratio of particle to fluid and the shear Reynolds number. The particle equilibrium positions for the linear shear flow are compared with those computed for Poiseuille flow conditions. Based on the numerical simulation results, a correlation has been derived between the particle-fluid density ratio and the critical particle Reynolds numbers needed to lift the particles. The effects of particle rotation and shape on the equilibrium position have also been studied by simulating the motion of rectangular particles. (C) 2003 Elsevier Science Ltd. All rights reserved.