Simulation of Soil-Structure Interaction becomes more and more the focus of computational engineering in civil and mechanical engineering, where FEM (Finite element Methods) for structural and soil mechanics and Finite Volume for CFD are dominant. New formulations have been developed for FSI applications using ALE (Arbitrary Lagrangian Eulerian) and mesh free methods as SPH method, (Smooth Particle Hydrodynamic). In defence industry, engineers have been developing protection systems for many years to reduce the vulnerability of light armoured vehicles (LAV) against mine blast using classical Lagrangian FEM methods. To improve simulations and assist in the development of these protections, experimental tests, and new numerical techniques are performed. To carry out these numerical calculations, initial conditions such as the loading prescribed by a mine on a structure need to be simulated adequately. The effects of blast on structures depend often on how these initial conditions are estimated and applied. In this report, two methods were used to simulate a mine blast: the classical Lagrangian and the ALE formulations. The comparative study was done for a simple and a more complex target. Particle methods as SPH method can also be used for soil structure interaction.