We study the problem of subtrajectory alignment over massive-scale trajectory data. Given a collection of trajectories, a subtrajectory alignment query returns new targeted trajectories by splitting and aligning existing trajectories. The resulting functionality targets a range of applications, including trajectory data analysis, route planning and recommendation, ridesharing, and general location-based services. To enable efficient and effective subtrajectory alignment computation, we propose a novel search algorithm and filtering techniques that enable the use of the parallel processing capabilities of modern processors. Experiments with large trajectory datasets are conducted for evaluating the performance of our proposal. The results show that our solution to the subtrajectory alignment problem can generate high-quality results and are capable of achieving high efficiency and scalability.