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We analyze the insurance of nuclear liability risk, from theoretical and applied standpoints. Firstly, we characterize the optimal insurance scheme for a low-prob-ability industrial accident, such as a nuclear catastrophe, when liability is shared between the firm and the State. Using catastrophe bond data, we then evaluate the cost of capital sustaining such an insurance mechanism. Finally, we characterize the individual lotteries associated with the risk of a nuclear accident in France, and we estimate the optimal coverage. We conclude that the liability limit currently in force is likely to be inferior to the socially optimal level.