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.