As numerical ocean simulations become more realistic, analysis of their output is increasingly time consuming. As part of a larger effort to make ocean model output more accessible for analysis, we have developed a fast particle-tracking algorithm for exploring the kinematics of the simulated flow. The algorithm is independent of operating system and fully vectorized and parallelized. Furthermore, it enables sliding of particles along solid boundaries according to the 3D along-boundary flow field. The new algorithm can easily simulate several million particle trajectories, thus opening the way for Lagrangian analysis of large-scale and multi-time scale oceanic phenomena.