The element-free Galerkin (EFG) method was used to simulate particle motion in two-phase flows with a new node distribution arithmetic suitable for meshless methods. The control equations were discretized with the standard Galerkin method in space and a fractional step finite element scheme in time. Regular background cells were used for the quadrature. The forces of the fluid on the particles were obtained by integrating the stress and shear forces on the particle surfaces. Simulation of the movement of a particle in a channel showed the Karman vortex street forming behind the particle with increasing particle velocity. Simulation of the movement of two particles in a channel showed the well-known drafting, kissing and tumbling, which has been obtained experimentally. Multi-particle flows were simulated with the results showing that meshless methods are capable of dealing with real particle collisions, which makes meshless methods superior to all mesh-based methods. Moreover, the theoretical relation of interparticle collision rate derived using kinetic theory was compared with the present numerical results and it is found that the collision rate is much lower than the theoretical estimation based on kinetic theory. (C) 2008 Elsevier Ltd. All rights reserved.