Bayesian inference allows the transparent communication of uncertainty in material flow analyses (MFAs) with the uncertainties reduced as newly collected data are included. However, the method is undermined by the difficultly of defining proper priors for the MFA parameters and quantifying the noise in the collected data. We start to address these issues by first deriving an expert elicitation framework suitable for generating MFA parameter priors. Second, we propose to learn the data noise concurrent with the parametric uncertainty. These methods are demonstrated using a case study on the 2012 U.S. steel flow. Eight experts were interviewed to elicit distributions on steel flow uncertainty from raw materials to intermediate goods. The experts’ distributions were combined and weighted depending on the expertise demonstrated in response to seeding questions. These aggregated distributions form our model priors. MFA data were then collected from the United States Geological Survey (USGS) and the World Steel Association (WSA) which are pub- lished without uncertainties. A sensible, weakly-informative prior was used to describe data noise. Bayesian inference was used to update the parametric and data noise uncertainty. The results show the reduction in MFA parametric uncertainty when incorporating the collected data. Only a modest reduction in data noise uncertainty was observed; however, greater reductions were achieved when using data from multiple years in the inference. These methods generate transparent MFA and data noise uncertainties learned from data rather than based on input uncertainty assumptions, providing a more robust basis for decision-making that affects the system.