The Material Point Method (MPM) is highly effective for modeling problems where the domain undergoes significant changes in configuration. In the specific case of water motion in a tank, MPM can accurately represent the dynamic response, including fluid heights against the tank walls, free surface position, natural frequency, and others. However, the computation of pressures (volumetric deformations) is prone to sources of instability due to the incompressible or quasi-incompressible nature of the fluid, leading to significant errors. The aim of this study is to adequately represent both the kinematics and the pressure evolution in the fluid under dynamic actions. To achieve this, two numerical methods were combined into a “B-Splines” MPM model: the Fractional Step Method [1] and the Affine Particle in Cell Method [2]. The results of a shaking table test conducted on a rigid water-filled tank subjected to a sinusoidal acceleration history in the longitudinal direction of the tank was used as a case study. The comparison between the numerical model's results and the laboratory test demonstrates that both the water's kinematics and the pressure evolution during the motion are adequately represented.