Fluid-structure interactions play an important role in many different types of real-world situations and industrial applications involving large-structural deformation and material or geometric nonlinearities. Numerical problems due to element distortions limit the applicability of a Lagrangian description of motion when modeling large deformation processes. An alternative technique is the multi-material Eulerian formulation for which the material flows through a mesh, fixed in space and each element is allowed to contain a mixture of different materials. The method completely avoids element distortions and it can, through an Eulerian-Lagrangian coupling algorithm, be combined with a Lagrangian description of motion for parts of the model. The Eulerian formulation is not free from numerical problems. There are dissipation and dispersion problems associated with the flux of mass between elements. In addition, many elements might be needed for the Eulerian mesh to enclose the whole space where the material will be located during the simulated event. This is where the multi-material arbitrary Lagrangian-Eulerian (ALE) formulation has its advantages. By translating, rotating and deforming the multi-material mesh in a controlled way, the mass flux between elements can be minimized and the mesh size can be kept smaller than in an Eulerian model.