A wide range of programs used to model mass movements currently exist.
In this chapter, we provide an overview by presenting a selection
of approaches used for modeling flows (e.g., debris flows and hyperconcentrated
flows) and falls (e.g., rockfall). Mass-movement models support the
study of geomorphic landscape changes, and, probably more importantly,
they are commonly used for natural hazard assessments in mountain
areas. As a first approach, the energy-line principle is widely applied,
but not all flow and fall processes can be simulated with this rather
simple method. Therefore, dynamic, process-based models have been
developed, each one adapted to specific mass-movement problems. The
energy-line principle is explained and models based thereon as well
as modeling problems presented. Then, models and modeling approaches
are introduced, which are used to describe mass flows with equations
of motion and continuity. Rockfall is commonly modeled by trajectory
models, which are explained theoretically and illustrated with an
applied example. This state-of-the-art chapter on numerical modeling
of flows and falls is followed by a discussion on future challenges
in mass-movement modeling.