The mechanism of train derailment is demonstrated to be the loss of the lateral vibration stability of train-bridge (track) system. Based on the theory of energy increment analysis for system movement stability, the method of stability analysis of lateral vibration for train-bridge (track) system and the energy increment criterion for derailment evaluation are put forward. The method of analyzing critical speed of train derailment is proposed on the basis of the energy increment criterion for derailment evaluation. The critical speed of freight train derailment on Youshui bridge and Laoluanhe bridge are calculated as 66.5 km/h and 65.2 km/h respectively, which are close to actual derailment speed 70 km/h. It is manifested that the method of stability analysis of lateral vibration for train-bridge (track) system is reasonable. The critical speed of train derailment on the Yanconggou bridge of Jingtong line are calculated as 73.0 km/h, and the results has provided important reference for operation department to take appropriate measures.