The research of the sloshing (defined as being the oscillations of the free surface of a fluid inside of a container) has many applications in the automotive, naval and aerospace industry. In the automotive industry, the sloshing behavior in fuel tanks is part of an overall NVH research to design cars that run smoother and quieter. Sloshing in fuel tanks typically occurs during the acceleration or braking of the vehicle, where the inertia make the fluid to move abruptly inside of the tank, generating undesirable noises to the passengers. The sloshing research allows knowing the fuel motion inside the tank, becoming possible to reduce the level of noise generated from the interaction of the fluid with the tank, by an optimized project of the tank geometric, fuel bomb localization, and the introduction of baffles. The use of numerical simulation in the study of sloshing can become the validation process of the product less onerous, reducing the costs of “try out” procedures and increasing the trustworthiness. This work had as objective to simulate by Finite Elements Methods the sloshing in an automotive fuel tank, using formulation ALE (Arbitrary Lagrangian-Eulerian) by the Radioss software. The numerical results had been compared with the results obtained by the experimental test, resulting in a satisfactory correlation. This work represents an important step inside a general target, which is the evaluation of the acoustics emission caused by the fuel tanks sloshing.