To study trends in extreme precipitation across the United States over the years 1951–2017, we analyze 10 climate indexes that represent extreme precipitation, such as annual maximum of daily precipitation and annual maximum of consecutive five-day average precipitation. We consider the gridded data produced by the CLIMDEX project (http://www.climdex.org/gewocs.html), constructed using daily precipitation data. These indexes exhibit spatial and mutual dependence. In this paper, we propose a multivariate spatial skew-t process for joint modeling of extreme precipitation indexes and discuss its theoretical properties. The model framework allows Bayesian inference while maintaining a computational time that is competitive with common multivariate geostatistical approaches. In a numerical study, we find that the proposed model outperforms several simpler alternatives in terms of various model selection criteria. We apply the proposed model to estimate the average decadal change in the extreme precipitation indexes throughout the United States and find several significant local changes.