Flows with particles in suspension is still a challenging task important in many applications such as sedimentation, rheology and fluidized suspensions. The coupling between the suspending liquid flow and the particles’ motion is the central point in the complete understanding of these phenomena. Moreover, the study of the evolution of the configuration of particles at an interface between two immisible fluid phases is also a very important research area, since it occurs in many engineering and industrial processes like slurries transport and drying processes of micro and nano suspension coating. This work proposes a new fictitious domain formulation based on Lagrange multipliers that solves the Navier–Stokes and rigid body equations to perform the simulation of the flow and of the flotation of particles embedded on one or more immiscible fluid phases that we numerically discretize using a fully implicit and coupled finite element approach. The method is validated using different test problems. The results obtained are compared with previous works, and the agreement is excellent.