Abstract: The element free Galerkin method (EFG) was used in the direct numerical simulation of multi-phase flows.Forces acting on particles were calculated by integrating the pressure and shear forces over particle surfaces.In the simulation of one particle’s falling process,it was found that a Karman vortex street was formed behind the particle with the increase of the particles’velocity and two particles’ falling process was simulated as well.The known drafting, kissing and tumbling phenomenon which was in agreement with experimental results was reproduced.In the simulation, EFG showed its advantage in dealing with particle’s collisions.The collision of a moving particle and a stationary cylinder was simulated and EFG was capable of dealing with real-contact collisions, while other methods based on meshes failed.Moreover, six particles’ falling process was calculated in this study.All these simulations showed that EFG could be applied to the large-scale direct numerical simulation of multiphase flows.