Arctic waters have historically been regarded as harsh environments owing to their extreme weather conditions and remoteness from land. The advantages of shorter sea routes and hydrocarbon energy exploitation have recently led to increased marine activities in such harsh environments. To ensure safe operation within the area, the potential risks of ship accidents, need to be systematically analyzed, assessed and managed along with the associated uncertainties. The treatment of epistemic uncertainty in the likelihoods of adverse events due to lack of knowledge and information should also be considered. This paper presents a Frank copula-based fuzzy event tree analysis approach to assess the risks of major ship accidents in Arctic waters, taking uncertainty into consideration. The quantitative approach includes four steps, namely, accident scenario modeling by an event tree model, probability and dependence analysis of the associated intermediate events, risk assessment with respect to the consequent outcome events. A major ship accident in Arctic waters - ships stuck in ice, is chosen as a case to interpret the modeling process of the approach proposed. Crews and ships owners can use such approach to defining risk control options that enable optimal risk mitigation. Maritime management may also benefit from better risk assessment.