综述了列车脱轨的国内外研究现状；分析了脱轨研究中的主要问题为：各国制订的规范标准不能预防列车脱轨，未抓住主要矛盾，脱轨计算理论存在三个根本问题——列车轨道(或桥梁)时变系统振动方程组解的唯一性无保证，横向振动的激振源不清楚，该时变系统振动的随机分析问题未解决；提出了一条突破列车脱轨难题的能量随机分析道路、预防脱轨措施及抗脱轨安全系数的计算方法；计算了四个列车脱轨实例，计算结果均与实际发生的脱轨事故和脱轨试验测出的车辆振动响应符合。

The present studies at home and abroad of train derailment are summarized. The following main problems in derailment research are analyzed: train derailment can not be prevented by the normal standards mapped out by each country; the main problems are not grasped; three fundamental problems — the sole solution to the vibration equation group of train-track (or train-bridge) time-varying system is not guaranteed; the excitation source of lateral vibration of the system is not clear; the problem of random analysis of this system is not solved — still exist in calculation theory of train derailment. The approach of random energy analysis, the breakthrough in solving the problem of train derailment, is presented. Preventive measures of train derailment and the calculation method of safety coefficient against derailment are introduced. Finally, four actual instances of train derailment are calculated and the results are in conformity with the actual accidents of derailment and with car vibrations tested by derailment experiments.