This research concerns the formulation of models and methods for supply chains risk analysis. An ontological approach using the KOD method (Knowledge Oriented Design) has been implemented to clearly identify relationships between the concepts of supply chain, risk, vulnerability and disturbances (critical scenarios). As a result, conceptual models of supply chains facing risk situations and critical scenarios are proposed. From the resulting conceptual models and mathematical models proposed in the literature, a multi-stage supply chain model using ARIMA models incorporating the randomness of the demand has been elaborated. In order to adapt this model to scenario criticality, constraints on orders and inventories have been taken into account. Under critical disturbances on information flows (demand) and physical flows (quality of the product supplied), constraints can be reached and supply chain behaviours can evolve toward critical dynamics or even become unstable. Supply chain vulnerabilities has been assessed and discussed.