Material flow analysis (MFA) is widely used to study the life cycles of materials from production, through use, to reuse, recycling, or disposal, in order to identify environmental impacts and opportunities to address them. However, development of this type of analysis is often constrained by limited data, which may be uncertain, contradictory, missing, or over-aggregated. This article proposes a Bayesian approach, in which uncertain knowledge about material flows is described by probability distributions. If little data is initially available, the model predictions will be rather vague. As new data is acquired, it is systematically incorporated to reduce the level of uncertainty. After reviewing previous approaches to uncertainty in MFA, the Bayesian approach is introduced, and a general recipe for its application to material flow analysis is developed. This is applied to map the global production of steel using Markov Chain Monte Carlo simulations. As well as aiding the analyst, who can get started in the face of incomplete data, this incremental approach to MFA also supports efforts to improve communication of results by transparently accounting for uncertainty throughout.