The Analytical Hierarchy Process (AHP) is a decision-making method capable of handling qualitative and quantitative elements. In this work, it is used to estimate the Failure Probabilities (FPs) of safety barriers (technical, procedural and organizational), within the framework of risk assessment of an oil and gas upstream plant. The barriers are modelled by a multistate Bayesian Network (BN) and FPs are defined for each barrier relative to their Health States (HSs). Expert elicitation procedures are adopted for feeding the AHP and a practical illustration is provided with regards to the safety barriers of the slug catcher of the upstream plant.