Cognitive scientists have begun collecting the trajectories of hand movements as participants make decisions in experiments. These response trajectories offer a fine-grained glimpse into ongoing cognitive processes. For example, difficult decisions 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 correlated 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 derivatives (e.g., velocity and acceleration) rather than a summary statistic. We show how Gaussian process regression can be implemented hierarchically across conditions and subjects, and used to model the actual shape and covariance of the trajectories. Finally, we demonstrate how to construct a generative hierarchical Bayesian model of trajectories using Gaussian processes.