The formulation and solution to the newsvendor problem using a Bayesian approach is presented. This approach allows us to incorporate the uncertainty in the parameters of demand distribution (introduced in the process of parameter estimation). An example that allows obtaining an analytical solution is presented and experiments are performed with the model in order to compare the results using the proposed Bayesian approach versus the classical method. In addition, the optimal order size is determined using stochastic simulation, methodology that is suggested when model complexity does not allow obtaining an analytical solution.