The automatic recognition of geometric constraints in virtual assembly and maintenance operations relies in the determination of intersecting surfaces between virtual prototypes. This is a key challenge in many virtual prototype applications, where it is necessary to find collisions precisely and interactively. This paper presents a novel algorithm to determine intersecting surfaces at interactive speed in a virtual prototyping environment. The proposed algorithm is based on the Overlapping Axis-Aligned Bounding Box (OAABB). The OAABB concept is used effectively to eliminate the number of surfaces that cannot intersect and improve performance. The algorithm also facilitates the implementation using parallel computing methods. OpenMP is used, taking advantage of shared memory multiple processors and reducing the overall time complexity of the collision detection algorithm. To achieve an efficient parallel simulation, it is necessary to provide an efficient load balancing scheme. Our experiences in parallelising the code to achieve a better work distribution are also described. Results show that the proposed collision detection achieves interactive rates in real industrial applications as desired.