This paper presents a fast method for determining an approximation of the local penetration information for intersecting polyhedral models. As opposed to most techniques, this algorithm requires no specific knowledge of the object's geometry or topology, or any pre-processing computations. In order to achieve real-time performance even for complex, nonconvex models, we decouple the computation of the local penetration directions from the computation of the corresponding local penetration depths: for any pair of intersecting objects, we partition the penetrating zones into coherent regions, and we determine for each of these regions a local penetration direction. Then, for each of these regions, we estimate a local penetration depth in the previously computed penetration direction. This method has been implemented and tested on a 2.0 GHz Pentium PC with a NVIDIA GeForce FX 5900 graphics card with AGP 4× and 768MB of RAM. The examples indicate that a meaningful local penetration information can be computed for complex models and challenging intersection scenarios within a few milliseconds.