We present a novel parallel algorithm for fast continuous collision detection (CCD) between deformable models using multi-core processors. We use a hierarchical representation to accelerate these queries and present an incremental algorithm that exploits temporal coherence between successive frames. Our formulation distributes the computation among multiple cores by using finegrained front-based decomposition. We also present efficient techniques to reduce the number of elementary tests and analyze the scalability of our approach. We have implemented the parallel algorithm on 8 core and 16 core PCs, and observe up to 7X and 13X speedups respectively, on complex benchmarks. Key words: Continuous collision detection, Deformable models, Parallel collision detection, Bounding volume hierarchies