||Simulation of soil structure interaction problems becomes more and more the focus of computational engineering in the last decades in the civil engineering community. In many applications in civil engineering, the Lagrangian formulation is the main approach for soil structure interaction problems. For the last decades, various approaches have been investigated in fluid and structure mechanics, to solve fluid structure interaction problems, including Arbitrary Eulerian Lagrangian (ALE) formulation and meshless methods as Smoothing Particle Hydrodynamics (SPH). These two approaches are more common in fluid mechanics than structure and civil engineering, where the classical Lagrangian formulation is still dominant for numerical simulations. The Lagrangian formulation, where the mesh moves with material is mainly used to solve problems in solid mechanics, and civil engineering for soil structure interaction problems. For small deformation, Lagrangian formulation can solve soil structure interface and material boundary accurately; the main limitation of the formulation is high mesh distortion for large deformation and moving structure. One of the commonly used approaches to solve these problems is the ALE formulation which has been used with success in the simulation of fluid structure interaction with large structure motion such as sloshing fuel tank in automotive industry and bird impact in aeronautic industry. In this paper, devoted to ALE formulation for civil engineering problems, the mathematical and numerical implementation of the ALE formulation and the contact algorithm are described. In order to validate the ALE algorithms, and prove its ability for civil engineering applications, we consider two different applications. First we perform the simulation of a shock wave propagation generated by a detonation of an explosive. In the second application, we consider a soil structure coupling problem, using an ALE formulation for the soil which undergoes large mesh deformation, and a Lagrangian formulation for the structure. A contact algorithm is performed at the soil structure interface.