The introduction of the article gives a short historical overview of the modelling of multi-body dynamics with unilateral contacts. The unilateral contacts formulation as introduced by Pfeiffer and Glocker is adapted to discretely defined body shapes. By using two-step collision detection, a fast and exact collision detection is achieved. The procedures are tested on a numerical example of the woodpecker toy and the results are compared with those of other authors who used a simpler mathematical model.