This paper is interested in investigating the buffer stock problem of a food supply chain during the Avian Influenza crisis possessing two originalities: a singular structure (forty-day upstream push and twenty four-hour downstream pull) and suffering from simultaneous fluctuations of raw material supply capacities (due to epizooty) and customer demand (due to customer anxieties and fears) resulted from sanitary crisis. At the theoretical level, we could not limit this case to a buffer optimization problem using a multiple period newsvendor model because of the non-linear feedback loops and exponential time delays in this food supply chain. Therefore, a simulation model basing on the system dynamics principles of Forrester (1961) allowed us to understand buffer size choices and smoothing production policies in this particular supply chain