The economic consequences of livestock epidemics have been long studied for purposes of estimating the costs of the veterinary measures. In this paper, we show that this catastrophic risk may have wide market consequences, and that the risk management systems are quite limited to compensate long term impacts in the European context of growing trade. Through a detailed literature review we present the main developments of the economic literature aiming to highlight the economic consequences of animal epidemics such as Foot and Mouth Disease. We acknowledge that a very few studies have focused on the economic dynamics and on the long run effects occurring after an epidemic disease outbreak. We discuss the appropriateness of a dynamic approach to reveal that the de-structuring of the livestock markets affects the production dynamics as well as the whole agricultural sphere, whose financial implications remain poorly studied. In addition, we highlight the importance of taking into account these phenomena for the development of risk management systems, and we emphasize the growing interest of a dynamic Computable General Equilibrium approach.