(Abstract) Analysis and matching of motion trajectories is needed to support recognition of motions and activities of objects in videos. In this paper, we introduce a new representation for modeling and matching motion trajectories. We model a trajectory as a continuous dense flow field from a sparse set of vector sequences using Gaussian Process Regression. We also introduce a random sampling strategy for learning stable classes of motions from limited data. Our representation allows for incrementally predicting possible paths and detecting anomalous events from online trajectories. It also supports for matching of complex motions with acceleration changes and stops within a trajectory. We use the proposed approach for classifying and predicting motion trajectories in traffic monitoring domains and test on several data sets. We show that our approach works well on various types of complete and incomplete trajectories from variety of video data sets with different frame rates.