Gravity hazards are a major concern to those living in mountainous areas. To protect infrastructure and human life in these areas, engineers require numerical tools for trajectory analysis, for application from fragmental rockfalls to large-scale avalanches or landslides. This book explores state-of-the-art methods to model the propagation (flows and stops) of masses, using the discrete element method (DEM) to study the evolution of kinetics during an event. Taking into account the shape of the blocks and the topology of the terrain provides an explicit and sophisticated consideration of geometries, eliminating the need for stochastic inputs to rockfall simulations. This method is validated experimentally, before the authors apply it to real case studies. The book ends with an introduction to and comparison with the material point method (MPM), a new and promising approach able to bridge the gap between cases dominated by discreteness and those involving a very large number of elements. Engineering consulting firms, researchers and students should find the approaches outlined in this book useful, whether designing prevention and protection systems for gravity hazards, or exploring new ways to model gravity hazards.