In this work we present and evaluate a novel 3D approach to track single people in surveillance scenarios, using multiple cameras. The problem is formulated in a Bayesian filtering framework, and solved through sampling approximations (i.e. using a particle filter). Rather than relying on a 2D state to represent people, as is most commonly done, we directly exploit 3D knowledge by tracking people in the 3D world. A novel dynamical model is presented that accurately models the coupling between people orientation and motion direction. In addition, people are represented by three 3D elliptic cylinders which allow to introduce a spatial color layout useful to discriminate the tracked person from potential distractors. Thanks to the particle filter approach, integrating background subtraction and color observations from multiple cameras is straightforward. Alltogether, the approach is quite robust to occlusion and large variations in people appearence, even when using a single camera, as demonstrated by numerical performance evaluation on real and challenging data from an underground station.