We consider a system of rigid bodies subjected to some non penetration conditions characterized by the inequalities f(alpha)(q) >= 0, alpha epsilon {1, ... , nu}, nu >= 1, for the configuration q epsilon R-d. We assume that there is no adhesion and no friction during contact and we model the behaviour of the system at impact by a Newton's law. Starting from the mechanical description of the problem, we derive two mathematical formulations, using either the configuration or the generalized velocity as unknown. Then a velocity-based time-stepping scheme, inspired by the catching-up algorithms, is presented and its convergence in the multi-constraint case (i.e nu >= 1) is stated.