This paper gives a presentation of the version of Kriging (BK) and Simulations (SK) with Bayesian guess of the drift coe cients. In particular, it shows that BK stands between the Simple Kriging (SK) where the drift is assumed to be known and the universal Kriging (UK) where there is no prior information on the drift. This paper is heavily inspired by the course of Bayesian approach given by Ch. Lajaunie during the Automnales at the Centre de Géosciences of the Ecole des Mines de Paris in Fontainebleau. It also contains several references from a paper by Omre & Halvorsen [1].