Issues with the estimation of expanded uncertainty in the fi rst draft of the revised Guide to the Expression of Uncertainty in Measurement (GUM) based on the Bayesian approach are considered. Comparative analysis is done of the methodologies that are known and those that are proposed by the authors for estimating expanded uncertainty, based on the current version of the GUM, the GOST R 8.736–2011 standard, and the distribution law of expanded uncertainty. It is shown that the authors’ technique makes it possible to achieve good correspondence of the estimates of expanded uncertainty with estimates obtained by the Monte Carlo method.