When subjected to dynamic excitations, liquid-filled tanks are particularly prone to sloshing, a phenomenon that can become critical in rockets, tank trucks or liquid storage facility, where it may lead to a loss of control or ultimate damage. A common mitigation strategy is to introduce internal baffles in order to attenuate fluid motion. A numerical method is developed to address a general sloshing problem while accounting for the discontinuity in the pressure field induced by an internal tank baffle modeled as a shell. The approach relies on a partition of unity strategy (XFEM), which eliminates the need for remeshing and rebuilding of operators for each baffle position and shape. This feature enables an efficient geometric parametrization and greatly facilitates subsequent optimization procedures.The proposed method is implemented for a three-dimensional fluid and validated on a parallelepiped tank sloshing problem with an internal baffle under harmonic excitation.