Context. The topical approaches to preventive estimations and mathematical modeling of cyber attacks processes and supply of external technological informational threats were considered, which may be directed on the physical security system of modern nuclear power plant units.Objective – is an adaptation of known mathematical models of cyber attacks kinetics for use in the system of information security and physical protection of nuclear power plants to modern and foreseeable conditions.Method. The method of model dependencies adaptation was proposed, which reflects the kinetics of cyberattacks to the modern operating conditions of protected nuclear facilities was proposed. To improve the model dependencies it was proposed to modify the classic Ferhulst function and, in mathematical modeling of cyber attacks on nuclear power facilities, to use the appropriate transformation of the logistic curve, which has distinctive feature of a well-defined maximum.Results. It was predicted that the model dependence of flow external to NPP cyber threats can be characterized by the alternation of maxima and minima, which indicates the possibility of an oscillatory character of the developing process. Also was put forward and substantiated the hypothesis that the system of physical and, in particular, cybernetic, NPP protection can be characterized by a time lag that in view of possible oscillatory character of information threats admissions process creates the preconditions for the development of oscillatory instability.The results obtained in the research are of applied nature, they can be used to carry out large-scale experiments and forecasting parameters of possible cyber threats aimed at the NPP for the purpose of pre-emption and preventive maintenance of information safety of modern nuclear energy technologies.Conclusions. Recommended for use model dependences were first adapted to the conditions of operating conditions of nuclear powerfacilities, take into account the factors to counter threats and circumstances associated with a specific time delay.It was shown for the first time that there is an opportunity both extreme and oscillatory dependence nature of the cyber attacks intensity, which are focused on software and hardware system of NPP information safety. The new approach allows to assume the reality of the unstable oscillation process in the “attack – defense” system and provides an opportunity of preventive assessment of the stability stocks.The practical significance lies in the fact that the results allow to realistically assess the time of onset of expected cyber attacks current dependence changes and to use this knowledge for organizational and technical preparation of remedies and early anticipation of IT-threats.