Introduction (problem statement and relevance). The insurance of the required safety level is getting more relevant in connection with the intensive implementation of remote control systems being developed for vehicles with varying degrees of motion autonomy. When transporting bulky and heavy loads off-road by remote-controlled tracked trains it is advisable to use the methods of full-scale mathematical modeling at the design stage to evaluate the operational properties of the remote-controlled tracked trains associated with undetermined actions of the driving operator.The purpose of the study was to evaluate the controllability of caterpillar trains transporting goods off-road with the help of a natural-mathematical modeling complex.Methodology and research methods. To assess the controllability of caterpillar trains, the mathematical model requirements for a complex of full-scale mathematical modeling were worked out, taking into account the mathematical model of caterpillar train motion. Using the method of natural-mathematical modeling, the controllability of a caterpillar train was evaluated when moving along a “snake” type trajectory.Scientific novelty and results. The methods presented in this paper and the developed mathematical model, suitable for a complex of natural-mathematical motion modeling, allow to determine the indicators of tracked trains operational properties associated with non-deterministic control actions of the driver operator and the disturbing effect of the road conditions. The novelty of the work lies in the developed mathematical model and the possibility of its application in the complex of natural-mathematical motion modeling for the study of operational properties and load modes of unmanned tracked trains. As a result of the study, the caterpillar trains controllability evaluation has been made when moving along a “snake” type trajectory as well as assessment of the caterpillar trains transmission load.Practical significance. The developed mathematical model allows determining the indicators of caterpillar trains operational properties at the design stage using a complex of natural-mathematical motion modeling. In addition, when performing virtual races, one can get data on the modes of transmission and select required characteristics.