Flood defences are becoming increasingly vital for protecting key coastal infrastructure from rising sea levels and storm surge waves. Waves attenuate rapidly as they propagate through porous media, corresponding to significant energy dissipation. The ability of porous armour layers to absorb wave energy is therefore of great interest to hydraulic engineers, as more and more natural and artificial porous structures are constructed to defend vulnerable coastlines or existing flood defences from wave attack. Design parameters for permeable flood defences include the grain size of the sediment particles that form the barrier and the width of the barrier. Previous studies have demonstrated that the runup height, which determines the risk of overtopping, is primarily dependent on the still water depth, wave amplitude and ground slope. This thesis investigates the effect of manipulating the mean grain size of a permeable barrier on the runup response to a dam-break flood wave and a solitary wave using the Material Point Method (MPM). Traditional methods for ascertaining the stability of protective barriers have used small-scale physical models, however, these are expensive and have been shown to suffer from scaling problems. Numerical methods are therefore gaining popularity in flood risk management applications. MPM is capable of handling large deformation problems within a Lagrangian framework, allowing for simple application of boundary conditions. MPM has been widely used to solve solid mechanics problems with history-dependent variables, but the application of this method to fluid mechanics has been rare. In MPM, the background mesh is only used to solve the governing equations. The material properties are stored at the material points so that issues arising from mesh distortions such as those exhibited in the classical finite element method (FEM) are easily avoided when coping with large deformations. Although it stores no permanent information, the background mesh allows for simple application of boundary conditions. Boundary conditions can be applied directly at the nodes, unlike in meshfree methods such as SPH where boundary conditions must be applied to a series of "boundary particles", which much first be identified. In single-point MPM, both the liquid and solid velocity fields are tracked by a single material point. The double-point MPM introduces two sets of material points representing the solid phase and liquid phase separately, so that it is capable of capturing the relative acceleration between the water and the soil skeleton. It is therefore capable of accurately modelling situations where the fluid moves significantly with respect to the soil, such as in wave run-up on structures. The goal of this research is to determine the effectiveness of sloped and vertical permeable barriers on preventing flooding resulting from storm surges and tsunami waves, and to ascertain the most effective permeability for reducing wave impact, to provide design guidance for coastal flood barriers. To this end, MPM is used to examine the influence of two key design parameters for porous, permeable flood defences, including the grain size of the composition particles and the width of the barrier. The term porosity is used to describe the dimensionless ratio of the volume of voids to solid material in the structure, and the term permeability is used to describe how resistant the porous structure is to flow, related to the mean grain size forming the material, in accordance with the Ergun equation used to determine the body force between the solid and liquid phases. This equation is presented in Chapter 3. A larger mean grain size results in larger voids in the material, so that there is less resistance to flow and the permeability increases. The multiphase version of the MPM package Anura3D (www.anura3d.com) has been adopted in this study. It is shown that increasing the grain size, and therefore the permeability, of the porous dam effectively reduces the overall runup height. The grain size, rather than the wall width, is shown to be the dominant parameter affecting the runup.