The dynamic response of a sloshing liquid to horizontal movements of a rectangular tank with a small amplitude is studied here by a numerical approach issued from a commercial CFD code. This numerical model solves Navier-Stokes equations considering a two-phase flow. In order to check the localized turbulence effects on the global fluid behavior, the averaged Navier-Stokes equations are solved with laminar option and with a k–ω SST turbulence model. The Volume Of Fluid (VOF) method is adopted to track the distorted free surface. The previous CFD solution is compared with a linearized approach based on the potential flow theory taking into account viscous effects. This model considers a single phase flow and is much less expensive in CPU time, especially thanks to the use of modal projection techniques. Both models are validated and applied on several cases. Free surface sloshing elevation and global forces, obtained for various excitation amplitudes and frequencies, are compared. Perfect and viscous liquids are considered.