Purpose. To solve the task of assessing the components of the guaranteed atmosphere air quality P MPj , P MP depending the maximum pollutant concentrations for a point source of emissions at the stage of designing in various industries (mining, metallurgical, chemical, electric power and others).Methods. The distribution of pollutant concentrations is represented as a vector random field, which at a given point of the area is turned into a vector random variable of concentrations and is characterized by a multi-dimensional density of distribution. To determine the density, the mathematical Berland's model of the concentrations distribution is applicable in Ukraine, in which the concentration arguments (design parameters of the source and environmental characteristics) are considered as random variables. Having assumed that the distribution density follows the normal law, using the method of function linearization of the random arguments based on the limit theorems of probability theory, its numerical characteristics have been obtained: mathematical expectations of concentrations, its mean square deviations, and correlation coefficients between concentrations. Findings.A new concept has been introduced of guaranteed air quality for populated areas. Based on predictive assessment, the studies have been carried out to ensure it at the stage of designing the facilities that have a point source of pollutant emissions. In accordance with the methodology, a mathematical model of the task of assessing and ensuring the guaranteed quality of atmosphere air has been obtained. According to the determination of the guaranteed atmosphere air quality, its measure is presented as a multi-dimensional probability integral of non-exceedance by the concentrations of at least one pollutant of its maximum one-time permissible concentrations with obtaining the numerical characteristics.Originality. As a result of studies, a mathematical model has been developed for the first time of the task of assessing and ensuring the guaranteed quality of atmosphere air, characterized by the probability values P MP , P MPj , when it is polluted by emissions from a point source. The control of the probability value P MP is performed by selecting the design source parameters so that its value is close to 1. Practical implications.The implementation of the developed model in construction projects with high probability, close to 1, ensures that at least one pollutant by its concentration will not exceed its normative maximum one-time permissible concentration, that is not implemented now. According to the maximum permissible concentration MPC MPj , determination, it is guaranteed the absence of the pollution effect on a person and the occurrence of corresponding diseases.