The work contains a theoretical study of freight car vibrations while a 12BM group of the freight cars are under braking by retarder.The purpose is to discover possible causes of derailment.The corresponding analytical description is presented.The solution of the differential equations for the groups of carriages confirms an assumption, according to which a contact between the carriage wheel of and the rail can be lost due to the oscillations induced by T-Shirts braking.The results allow to present recommendation for choosing the safe regime of braking in order to avoid the derailment.