This thesis aims to contribute to the understanding of how waves interact with soil. It is crucial for various applications in Civil Engineering to analyze the behaviour of soil and to understand the physics behind it. This master thesis contributes to this understanding via studying the impact of the boundary conditions on the model results with the aim of being able to model interaction between waves and soil. We assume a media that is poroelastic and fully-saturated, unless stated otherwise. We also assume that the porous media consists of incompressible soil particles and pore water particles that may either be compressible or incompressible. The main goals of this thesis are (1) to describe the response of porous media to transient hydraulic loads using numerical methods like the Finite-Element Method, and (2) to apply it to a one-dimensional case whereby a sandbed is subjected to waves. Currently, it is common to predict the changes in pore water pressures in porous media subjected to transient hydraulic loads using Biot’s model, which often assumes compressible pore water, assumes zero effective stresses on the surface of the seabed, and assumes that the wave load is completely carried by the pore water pressure only. Recently, a new model is proposed by Van Damme and Den Ouden-Van der Horst suggesting that transient hydraulic loads acting on a porous medium affect both the pore water pressures and effective stresses in soils. Note that this makes sure that the momentum balance equations are satisfied throughout the computational domain and its boundaries. The boundary conditions in this case do not satisfy Terzaghi’s effective stress principle, whereas the standard has been to impose Terzaghi’s effective stress principle when solving Biot’s equations. Terzaghi’s principle states that the sum of the effective stresses and pore water pressures must equal the hydraulic loads, whereas Biot’s model is in line with this principle. The model of Biot and the new model of Van Damme and Den Ouden-Van der Horst describe the physics differently which can have a large impact on the results. For example, the assumption of compressibility can significantly impact the distribution of the effective stress in the soil and thus the results. Biot’s model is more sensitive for changing the compressibility parameter than the new model. Both models give similar solutions to the water pressure. However, they give different solutions to the other variables like the volumetric strain and displacements which appear in both models. Furthermore, the new model in one dimension is in line with the momentum balance equations and satisfies the volume balance equation. On the other hand, the standard is to solve Biot’s model by imposing Terzaghi’s principle at the boundary. For the new model we found promising results for the water pressure, when validating with the data of two experiments. At the end, which model predict the best solutions for volumetric strain, water pressure and displacements depends on what kind of problem the model is used for and the corresponding physics. The used code can be found at https://github.com/fpmklein/Compressiblevs.-incompressible-pore-water-in-fully-saturated-poroelastic-soil.