This paper proposes a capital accumulation model with a random stopping time corresponding to the occurrence of an environmental catastrophe. Depending on the preventive capital stock accumulated at the time of the catastrophe, the damage cost associated with the catastrophe varies. The long-term behavior of the optimal accumulation path is analyzed using turnpike theory. The case where the catastrophe process is uncontrolled is distinguished from the case where there is an anthropogenic effect on the probability of an occurrence. Intergenerational equity issues are discussed. Numerical experiments with an adaptation of the integrated assessment model DICE94 are proposed to explore the model responses.