Purpose. Clarification of safety criteria of the wheels derailment from the rails using either the lateral or the directing force. Methodology. Technique is connected with the analysis of safety criteria expressions of the wheels derailment from the rails, which use the lateral or the directing force in the position of limit equilibrium of the system, as well as with the analysis of expressions for the coefficient of stability from the wheels derailment from the rails when using the specified criteria. Findings. It is shown that the safety criteria of derailment, representing either the ratio of the lateral force to vertical one or the directing force ratio to the vertical one, which operate in the contact point of the climbing wheel flange with the rail head, are equivalent. As for the stability coefficient of derailment, it is shown that near to the safety limit their use yields almost the same results. Originality. The concept of the safety criteria, using the lateral or directing forces is specified and their equivalence is shown. Practical value. Obtained results allow one to use one of these two safety criteria expressions instead of two expressions cited in the normative literature, which gives the number of advantages for the processing of testing results. And the recommendations on the use of criteria, in which the ratio of lateral or directing forces to the vertical force acting in the contact point of the climbing wheel flange with the rail head were given.