Cognitive scientists have begun collecting the trajectories of hand movements as participants make decisions in experi-ments. These response trajectories offer a fine-grained glimpse into ongoing cognitive processes. For example, difficult deci-sions show more hesitation and deflection from the optimal path than easy decisions. However, many summary statistics used for trajectories throw away much information, or are cor-related and thus partially redundant. To alleviate these issues, we introduce Gaussian process regression for the purpose of modeling trajectory data collected in psychology experiments. Gaussian processes are a well-developed statistical model that can find parametric differences in trajectories and their deriva-tives (e.g., velocity and acceleration) rather than a summary statistic. We show how Gaussian process regression can be im-plemented hierarchically across conditions and subjects, and used to model the actual shape and covariance of the trajecto-ries. Finally, we demonstrate how to construct a generative hi-erarchical Bayesian model of trajectories using Gaussian pro-cesses.