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A certain connection exists between the level of radon in the air and diseases of the human respiratory system. The prersent research evaluates the risk of disease incidence with oncologic lung illnesses and mortality rate from them on the account of exposure during the inhalement of internally in-built radon by the population in Rivne city dwellings.  We measured radon in 2011-2016 and used radonometer «Alfarad Plus». The method proposed by Covello and Merkhofer (1993) and NRC (1983) is used. In accordance with it, the assessment of mortality rate of city inhabitants from lung cancer due to internal exposure to radon was carried out in four stages. This, in particular, is the identification of population, the analysis and selection of the most optimal dependence of «dose-effect», the direct evaluation of radon influence on population and the calculated risk of lung cancer.  The measurement of radon concentration in premises in Rivne testify its substantial variability. The average geometric value of VA for basement premises amounts to 365 Bk/cub.m and for semi-basement premises-161 Bk/cub.m. The prognosticated maximum possible value of VA in buildings by results of our measurements is assessed as 1.420 Bk/cub.m.  Thus, the calculated expected shortening of life duration for population of Rivne by different models of DDE constitutes from 1.2 to 4.0 years for the whole population and from 2.5 to 7.41 years for those share of population who smokes. Keywords: Radon; coefficient of additional relative risk; exposure; lung cancer References: AFSSE-Impact sanitaire de la pollution atmosphérique urbaine. Agence Française de Sécurité Sanitaire Environnementale.-mai 2004-Rapport 1. 72 p. Available at: http://www.cancer-environnement.fr/Portals/0/Documents%20PDF/Rapport/Anses/Afsset/2004%20Impact_pollution_atmos_urbaine_rapport1.PDF Angell, W. J. (2008). The US radon problem, policy, program and industry: achievements, challenges and strategies. Radiation protection dosimetry, 130(1), 8-13. doi: 10.1093/rpd/ncn105 Arvela, H. (1995). Seasonal variation in radon concentration of 3000 dwellings with model comparisons. Radiation Protection Dosimetry, 59(1), 33-42. Available at: https://doi.org/10.1093/oxfordjournals.rpd.a082634 Baysson, H., Billon, S., Laurier, D., Rogel, A., & Tirmarche, M. (2003). Seasonal correction factors for estimating radon exposure in dwellings in France. Radiation protection dosimetry, 104(3), 245-252. Available at: https://doi.org/10.1093/oxfordjournals.rpd.a006188 Catelinois, O., Rogel, A., Laurier, D., Billon, S., Hemon, D., Verger, P., & Tirmarche, M. (2006). Lung cancer attributable to indoor radon exposure in France: impact of the risk models and uncertainty analysis. Environmental health perspectives, 114(9), 1361. doi:  10.1289/ehp.9070. Cohen, B. L., & Shah, R. S. (1991). Radon levels in United States homes by states and counties. Health physics, 60(2), 243-259. Available at: https://journals.lww.com/health-physics/Abstract/1991/02000/Radon_Levels_in_United_States_Homes_by_States_and.13.aspx Collection of indices of public health and activities of medical institutions of Rivne region for 2011-2015. Communal institution "Regional information-analytical center of medical statistics" of Rivne regional council, Rivne, 2016 [in Ukrainian]. Council of the European Union. (2014). Council Directive 2013/59/EURATOM of 5 December 2013 laying down basic safety standards for protection against the dangers arising from exposure to ionizing radiation. Brussels: O. J. EU. Available at: https://publications.europa.eu/en/publication-detail/-/publication/65527fd1-7f55-11e3-b889-01aa75ed71a1/language-en/ Accessed on 25.12. 2017 Covello, V. T., & Merkhoher, M. W. (2013). Risk assessment methods: approaches for assessing health and environmental risks. Springer Science & Business Media. http://www.fao.org/tempref/docrep/fao/010/i0035e/i0035e03.pdf Darby, S., Hill, D., Auvinen, A., Barros-Dios, J. M., Baysson, H., Bochicchio, F., ... & Heid, I. (2005). Radon in homes and risk of lung cancer: collaborative analysis of individual data from 13 European case-control studies. Bmj, 330(7485), 223. doi: https://doi.org/10.1136/bmj.38308.477650.63 (Published 21 December 2004). Darby, S., Hill, D., Deo, H., Auvinen, A., Barros-Dios, J. M., Baysson, H., Bochicchio, F., Falk, R., Farchi, S., Figueiras, A., Hakama, M., Heid, I., Hunter, N., Kreienbrock, L., Kreuzer, M., Lagarde, F., Mäkeläinen, I., Muirhead, C., Oberaigner, W., Pershagen, G., Ruosteenoja, E., Schaffrath, R. A., Tirmarche, M., Tomášek, L., Whitley, E., Wichmann, H. E., Doll, R. (2006). 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Investigation of volumetric activity of the radon of inland air of the city of Rivne. Bulletin of the Kremenchug Nat University named M. Ostrogradsky, 104(1), 124-129. [in Ukrainian]. Available at: http://www.kdu.edu.ua/PUBL/statti/2017_3_124-129_3-2017-1.pdf Kononenko, D. V. (2013). Estimation of Radiation Risk for the Population of St. Petersburg in Radon Radiation. Radiation Hygiene, 6(1), 31-37. [in Russian]. Available at: https://www.radhyg.ru/jour/article/view/73/89 Krewski, D., Lubin, J. H., Zielisnski, J. M., Alavanja, M., Catalan, V. S., Field, R. W., Klotz, J. B., Létourneau, E. G., Lynch, C. F., Lyon, J. I., Dale, P. S., Janet, B. S., Daniel, J. S., Jan, A. S., Clarice, W., Homer, B. W. (2005). Residential radon and risk of lung cancer: a combined analysis of 7 American case-control studies. Epidemiology, 16(2), 127-145. doi: 10.1097/01.ede.0000152522.80261.e3 Lebed, O. O., Klymenko, M. O., Lysytsya, A. V., & Myslinchuk, V. O. (2018). 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