Abstract: Fluid-Structure Interaction (FSI) is an engineeringproblem with many practical aspects such as the swash of seabed, thestagnation of contamination, the settlement of sand around coastalstructures, and the resonance of structures under internal/external currentexcitations. Many numerical schemes had been presented in the past twodecades. This paper deals with a finite element method to simulate theinteraction of a coupled incompressible fluid-rigid structure system. Basedon the Fictitious Domain (FD) method in the multi-phase flows field, a setof fully coupled FSI governing equations is presented. In this``monolithic'' approach, the structure is taken as ``fictitious'' fluid withzero strain rate and the whole computational domain is modeled by theNavier-Stokes equations. However, to keep the rigid body shape and behaviorsof the ``fictitious'' fluid, the Distributed Lagrange Multiplier (DLM)method is applied on this domain. The whole field, including fluid regionand structure region, is described by velocity and pressure, and the entireset of model equations is discretised with fixed Eulerian mesh. Three majoradvantages of the present formulation include: (i) The unitized governingequations both for fluid and structure help capturing the predominantphysics of interaction phenomena; (ii) The interfacial force/displacementbetween fluid and structure are internal actions for the overall system.Therefore, the stress/velocity consistency conditions on the fluid-structureinterface are automatically satisfied in this fully coupled model; (iii) Forthe using of fixed Eulerian mesh, it is not necessary to remesh thecomputational domain, and thus free from mesh distortions. Results fromnumerical simulations on particulate flow and FSI problems provideconvincing evidences for the model's high accuracy and the suitability forthe simulation of large-deformation/movement FSI problems.