By applying system dynamics stability concepts, the mechanism of train derailment on bridge is proposed. Then the theory of energy random analysis for train derailment on bridge is put forward. The contents of the theory are as follows: (1) Establishing of vibration equation set of the train-bridge system; (2) Determining of exciting source of transverse vibration of the system; (3) Method of random energy analysis of transverse vibration of the system; (4) Geometric rules of derailment; (5) Calculation of the whole courses of train derailment on bridge; (6) Criteria of energy increment for judging train derailment on bridge. Finally, three cases concerning trains derailment on bridges are made, which coincide with the actual conditions. Meanwhile, some main conclusions are also obtained as follows: (1) Insufficient of transverse rigidity of bridge is the reason causing train derailment on bridge. (2) Enhancing transverse rigidity of bridge is the main preventive measure against train derailment on bridge.
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