A methodology for risk analysis applicable to shipping in arctic waters is introduced. This methodology uses the Bowtie relationship to represent an accident causes and consequences. It is further used to quantify the probability of a ship accident and also the related accident consequences during navigation in arctic waters. Detailed fault trees for three possible ship accident scenarios in arctic transits are developed and represented as bowties. Factors related to cold and harsh conditions and their effects on grounding, foundering, and collision are considered as part of this study. To illustrate the application of the methodology, it is applied to a case of an oil-tanker navigating on the Northern Sea Route (NSR). The methodology is implemented in a Markov Chain Monte Carlo framework to assess the uncertainties arisen from historical data and expert judgments involved in the risk analysis.