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Risk evaluation of oil and natural gas drilling process is a challenging task, due to high uncertainty and ambiguity in the available data, as well as the complexity of technical processes. A systematic approach is required to handle both quantitative and qualitative data. Lack of data for calculating the failure rate of components is a common obstacle in the drilling industry. A proposed model using Fuzzy Risk Assessment (FRA) and AHP is presented for determining and prioritizing the aggregate risk for the scenario of Loss Of Circulation (LOC). A Fuzzy Analytical Hierarchy Process (FAHP) methodology is designed to deal with an alternative selection and justification problem by integrating the concept of fuzzy set theory and AHP. Risk Factors (RFs) in a hierarchical framework are expressed as fuzzy numbers which is a combination of the likelihood of a failure event and the associated failure consequence. AHP is used to estimate weights required for grouping non-commensurate risk sources. Probability and the severity of risk factors are expressed by multiple levels, qualitative scaling scheme using linguistic variables which are calculated through fuzzy numbers to reflect the subjective nature of risk definition. The risk mapping of risk factors on the fuzzy scale can help to figure out the dependency of each risk factor to the risk levels. By employing this model the critical risk factors in LOC are identified. As a result, the research can provide theoretical and practical contributions to drilling process safety and environmental protection.