The aim of this paper is to develop on discrete models that reproduce the behavior of a crowd of people in several emergency evacuation situations. The first step in this study is to determine how to treat contacts between pedestrians. For that, three already existing discrete approaches, one smooth and two non-smooth, originally proposed to simulate the collisions of granular assemblies, are first analyzed both from the theoretical and the numerical point of view. The solving algorithms are presented and the numerical formulation of the two non-smooth approaches is compared to standard plasticity in order to point out the common theoretical framework. The next step is to adapt these discrete approaches to represent pedestrians. The key point is to introduce a “willingness” for each particle through a specific desired velocity. These adapted discrete approaches are able to handle local interactions, like pedestrian-pedestrian or pedestrian-obstacle contacts, in order to reproduce the global dynamic of pedestrian traffic. Finally, results of several simulations in emergency configurations are presented as well as compared to real exercise ones.