The aim of the paper is to develop a fully 3D simulation technique for rockfall dynamics taking rock shape into account and using the state-of-the-art methods of multibody dynamics and nonsmooth contact dynamics. The rockfall simulation technique is based on the nonsmooth contact dynamics method with hard contact laws. The rock is modeled as an arbitrary convex polyhedron and the terrain model is based on a high resolution digital elevation model. A specialized friction law for rockfall is proposed which allows for the description of scarring behavior (i.e., rocks tend to slide over the terrain before lift-off). The influence of rock geometry on rockfall dynamics is studied through two well-chosen numerical simulations.