Introduction. Operation of radiation hazardous facilities is a reality of the modern world, and the future of the world economy is impossible without the development of nuclear and radiation technologies. At the same time, the widespread use of atomic energy puts forward an important and responsible task of ensuring the safety of the population and the environment in conditions of an increased risk of exposure to ionizing radiation and radioactive substances. In accordance with clause 3.2.1 of the "Radiation Safety Standards NRB-99/2009", the planned increased exposure of persons involved in emergency rescue operations related to the elimination of the consequences of radiation accidents is allowed for men, as a rule, over 30 years old only with their voluntary written consent, after informing about possible radiation doses and health risks. Increased exposure refers to exposure in excess of the basic dose limits under controlled (normal) operating conditions of radiation sources. Goals and objectives. The aim of the study is to increase the functionality of emergency services and fire and rescue subdivisions to perform tasks as intended in the elimination of radiation accidents. The tasks include the construction and substantiation of a model that allows converting the risks of deterministic effects into stochastic effects risks. Methods. When calculating the probability of output of stochastic and deterministic effects depending on the radiation dose and developing a threshold quadratic model, the least squares method and the probabilistic-statistical method were used. Results and discussion. The article shows that a linear non-threshold model of the interaction of radiation with matter greatly overestimates the risk of a stochastic effect emerging at doses of radiation. For example, this overestimation is 8,13 at a dose of D = 0,2 Sv/year. In this regard, a threshold quadratic model has been developed and proposed to be replaced by a threshold quadratic model, which makes it possible to increase the planned irradiation of personnel of emergency services and fire and rescue units during the elimination of radiation accidents in an effective dose from 0,2 Sv to 0,57 Sv, moreover, the probability of emergence of stochastic effects P2 = 0,0084 remains the same for both models. Conclusions. An increase in the maximum permissible dose of radiation for personnel of emergency services and fire and rescue units from 0,2 Sv/year to 0,5 Sv/year will make it possible to increase the functionality of the emergency services and fire and rescue units to perform tasks as intended by 2,5 times when elimination of radiation accidents. For example, the scope of rescue operations may be increased from 100 %, performed at a dose of D = 0,2 Sv/year, to 250 %, performed at a dose of D = 0,5 Sv/year. Key words: emergency services, fire and rescue units, radiation accidents, irradiation, linear no-threshold model, threshold quadratic model.