In this paper we propose a two-stage screening and analysis process for identifying multiple contingencies that may result in very severe disturbances and blackouts. In a screening stage we form an optimization problem to find the minimum change in the network to move the power flow feasibility boundary to the present operating point and that will cause the system to separate with a user-specified power imbalance. The lines identified by the optimization program are used in a subsequent analysis stage to find combinations that may lead to a blackout. This approach is applied to a 30-bus system with encouraging results.