This paper presents a probabilistic failure analysis of leakage of the oil and gas in a subsea production system using fault tree analysis (FTA). A fault tree was constructed by considering four major areas where the leakages can be initiated. These are: gas and oil wells, pipelines, key facilities and third party damage. Conventional FTA requires precise values for the probability of failure of the basic events. However, since the failure data are uncertain, a fuzzy approach to these data is taken which leads to the so-called fuzzy fault tree analysis (FFTA), a method that employs expert elicitation and fuzzy set theories to calculate the failure probabilities of the intermediate events and the top event through identification of the minimal cut sets of the fault tree. A number of importance measures for minimal cut sets and the basic events have been obtained which helps to identify the nature of dependence of the top event on the basic events and thereby can identify the weakest links that may cause leakage in the subsea production system.