<p>This paper studies the problem of Bayesian parameter estimation and dependence detection in the seemingly unrelated regression (SUR) models. We propose three sparse Bayesian SUR modeling methods via the Laplace prior and the horseshoe prior as well as their combination. The hierarchical Bayesian expressions for the Laplace and the horseshoe priors are obtained, and the full conditional posterior distributions for all parameters are also given for algorithm implementation. By imposing the shrinkage priors on the parameters of the transformed SUR models, the proposed three methods can simultaneously estimate the regression coefficients and detect the inter-model dependence. Simulation studies show that both the horseshoe prior and the combination of the Laplace prior and the horseshoe prior outperform the Bayesian SUR with the Laplace prior or DMC approach in detecting correlations and the variable selection in terms of mean squared error. Finally, a real data analysis demonstrates the effectiveness of the proposed methods.</p>