The dynamics of collections of bodies, treated as perfectly rigid, involves nonsmooth mathematical relations, arising from the unilaterality of impenetrability constraints, from the formulation of dry friction and from the velocity jumps produced by possible collisions. The presented numerical methods treat nonsmoothness without resorting to regularization procedures. The examples shown concern populations of balls contained is a vertically vibrated rectangular box. First, a comparison is made with some experiments pe1formed by other authors, about the paradoxical shape taken by the free surface when vibration is not strong enough to fluidize it. Other examples reveal an unexpected mechanism of size segregation.