We present a new parallel algorithm for interactive and continuous collision detection between deformable models. Our algorithm performs incremental hierarchical computations between successive frames and parallelizes the computation among multiple cores on current CPUs. The main computations include front building and updating and performing the elementary tests between the triangle primitives. The overall algorithm can perform inter- and intra-object collisions at interactive rates on current commodity processors on models with many tens of thousands of triangles. In practice, the performance of our algorithm almost scales linearly with the number of cores. Keywords Continuous collision detection, deformable models, multicore processor, parallel collision detection