||Multivariate analysis is preferred over univariate analysis in plant breeding studies because it can exploit correlated traits and environments, whereas Bayesian analysis provides a natural way to incorporate prior knowledge and inferences that are conditional on the observed data. The objective of this paper is to show how to use multivariate Bayesian analysis for estimating random effects of genotype x environment and genotype x environment x trait combinations, and for computing genotypic and phenotypic correlations among traits and environments. Data were collected from on-farm trials conducted by the International Maize and Wheat Improvement Center (CIM-MYT) to evaluate bread and durum wheat lines in the Yaqui Valley of southern Sonora, Mexico, during three crop seasons (2012, 2013, and 2015). The Bayesian multi-trait and multi-environment model with Gibbs sampler provides an analytic solution that can be used as an alternative for analyzing on-farm multiple-trait and multiple-environment data because it allows making parsimonious, precise and simultaneous estimations of random effects, genetic correlations (of traits and environments) and residual correlations of traits. The multivariate Bayesian model successfully fitted three of the four data sets (2012, 2015, and combined cropping seasons), but did not fit well the data of crop season 2013. For three out of five traits under study in this crop season, the correlations between the observed and predicted phenotypic values were lower than 0.6, suggesting that the predicted values were not very close to the observed values.