This article presents a method for the management of catastrophic risks generated by industrial activities. The multi-criteria decision-making tool which we have developed does not suffer from the same limitations as decision theory or the standard approach to risk assessment and management. Our quantitative risk analysis takes into account three factors: (1) the analysis of the relative acceptability of risks to society; (2) the minimization of the mathematical expectation of financial losses using a catastrophe aversion coefficient; and (3) the preference for flexibility expressed by industrial managers. This method has been applied to the comparison between two catastrophic risks on a French chemical site.