Zellner's idea of combining several equations into one model to improve estimation efficiency (Zellner 1962) ranks as one of the most successful and lasting innovations in the history of econometrics. The resulting seemingly unrelated regressions (SUR)model has generated a wealth of both theoretical and empirical contributions. With the recent explosion of literature on MCMC techniques, Bayesian inference in the SUR model has become a practical reality. However, it is the author's view that, prior to the writing of this chapter, the relevant results have not been collected and summarised in a form convenient for applied researchers to implement. It is my hope this chapter will facilitate and motivate many more applications of Bayesian inference in the SUR m