Abstract: This article shows how statistical motion priors can be combined seamlessly with physical constraints for human motion modeling and generation. The key idea of the approach is to learn a nonlinear probabilistic force field function from prerecorded motion data with Gaussian processes and combine it with physical constraints in a probabilistic framework. In addition, we show how to effectively utilize the new model to generate a wide range of natural-looking motions that achieve the goals specified by users. Unlike previous statistical motion models, our model can generate physically realistic animations that react to external forces or changes in physical quantities of human bodies and interaction environments. We have evaluated the performance of our system by comparing against ground-truth motion data and alternative methods.