Three fundamental problems in the calculation of train derailment abroad and at home were pointed out and the solutions to these problems were presented. The theory of random energy analysis for train derailment was suggested. The main contents of this theory are as follows: geometric criterion of derailment; method of random energy analysis of transverse vibration of train track system; mechanism of derailment and energy increment criterion for derailment evaluation; calculation of the entire derailment course of train. This theory is used to calculate a case of freight train derailment, which corresponds to an actually occurring accident. Another derailment test, in which the train is judged not to be derailed, is calculated and the maximum vibration response is well correspond to the test results. And the effectiveness and practicability of the theory are proved by the two calculated cases.