The article presents the principles of the method of operational investigation of rolling stock derailment. This method is intended to identify the most significant mechanical reasons for transport accidents in order to find directions to further improving the safety requirements for the state of maintenance of freight cars and tracks on the basis of the data. The developed method establishes a general methodological order of conducting computer simulation of the dynamics of rolling stock of multivariate studies on calculating the safety indicators of train’s motion, and shows the significance of technical factors that provoked a certain event. By this method, the operational investigation of rolling stock derailment is based on the development of adequate computer models of dynamics of cars in trains. In this case, in detail, all the features of the car, which descended from the rails, are first. The presented method is based on the principles of factor analysis, where the intervals of varying events are presented in natural units of measurement. In this case, the assessment of security indicators for each research of the experiment plan is also carried out taking into account their dimension. As a result, the function of multiple regressions on the chosen indicator of motion safety allows not only to determine the significance of the factor of the ascent, but also to establish the level of factors, with exceeding the criteria for motion safety, that is, to determine the boundaries of the region with an acceptable level of motion safety.