In recent years, the Material Point Method (MPM) has been applied to a number of geotechnical problems and has been extended to solve coupled flow-deformation problems. The dynamic formulation and the dual description of the media (lagrangian material points and an eulerian numerical mesh) provide the MPM the capabilities of handling problems involving large displacements and deformations. The paper presents four examples with the aim of highlighting the dynamic formulation and the capability of the method to analyze in a unified mathematical framework the static-dynamic transition of a slope failure.