Recently some building structures have collapsed because of losses of vertical load carrying capacities resulting from accidental events. in this paper, limit analysis called Compact Procedure is applied to some cases of collapsed structures and the key-elements in the structures are identified using Sensitivity Analysis. Two collapse prevention methods are discussed. For truss structures, the collapse can be prevented by reinforcement of members having sensitivity greater than 0.3-0.4. For frame structures, the relations between the sensitivity and the progressive collapse are defined using a safety factor and the progressive collapse can be prevented by fixing X braces into each span of the top floor. (C) 2009 Elsevier Ltd. All rights reserved.