This chapter presents some first steps towards the modelling of geocontainers with Material Point Method. Therefore, a series of elementary problems, for which an analytical solution exists, is presented in order to validate MPM before discussing the modelling of geocontainers. The elementary problems consist of one-dimensional (1D) wave propagation in dry soil, 1D wave propagation in saturated soil and 1D poroelastic flow. It presents the modelling of a simplified geocontainer. The time required for the wave to travel along the solid column is correctly captured as well as the average amplitude of the stress and velocity. This means that the second wave is only visible within the vicinity of the stress boundary condition, immediately after the application of the stress. This chapter presents the modelling of a 2D poroelastic solid flow, which resembles a simplified geocontainer installation process. The poroelastic solid velocity oscillates sinusoidally around the analytical flow velocity due to the liquid compressibility and element crossing.