In the work, as a research object, a protective device of a domed form is used which is used by pyrotechnic units to localize an emergency situation in the event of an explosion inside a small hazardous object. It is noted that one of the most problematic places of its application is the development of recommendations, implementation of which should ensure the prevention of the development of an emergency event up to a level of emergency on such priority effects as the number of victims and the number of victims. It is shown that the definition of such recommendations, providing localization of the consequences of an emergency in the case of an explosion of a small explosive object inside a specialized protective device, requires the obtaining of a mathematical model of localization of the focal point of an emergency. This model should provide an assessment of the strength of the technical means of localization of fragments and become the basis for the correction of existing operational procedures in the case of its application by pyrotechnic units. In the course of the study, the Eulerian-Lagrangian approach is used, which would allow obtaining a mathematical model of localization with the help of a dome-shaped form of the consequences of emergency situations in the event of an explosion inside a small-sized dangerous object. In practice, a mathematical model is implemented in a finite element packet using the library of the ANSYS/AUTODYN computer system. This allows not to create an actual new package of applications every time, as was done before to describe similar models. Due to this, an assessment of the strength of the technical means of localization of fragments is provided. In comparison with similar well-known models, the developed mathematical model allows to estimate the size of the minimum thickness of the protective device. It allows to withstand the explosion of a small-sized explosive object and to determine the minimum mass of the protective equipment taking into account the operational capabilities of the combat calculation of the pyrotechnic unit.