In order to understand the hydrodynamic interactions that can appear in a fluid particle motion, an original method based on the equations governing the motion of two immiscible fluids has been developed. These momentum equations are solved for both the fluid and solid phases. The solid phase is assumed to be a fluid phase with physical properties, such as its behaviour can be assimilated to that of pseudo-rigid particles. The only unknowns are the velocity and the pressure defined in both phases. The unsteady two-dimensional momentum equations are solved by using a staggered finite volume formulation and a projection method. The transport of each particle is solved by using a second-order explicit scheme. The physical model and the numerical method are presented, and the method is validated through experimental measurements and numerical results concerning the flow around a circular cylinder. Good agreement is observed in most cases. The method is then applied to study the trajectory of one settling particle initially off-centred between two parallel walls and the corresponding wake effects. Different particle trajectories related to particulate Reynolds numbers are presented and commented. A two-body interaction problem is investigated too. This method allows the simulation of the transport of particles in a dilute suspension in reasonable time. One of the important features of this method is the computational cost that scales linearly with the number of particles.