Purpose. The purpose of this article is to study the conditions for achieving high results of operational actions of rescue services and quality management, which will allow timely and correct choice of methods, forces and means of firefighting in coal mines and carry out operational maneuvers depending on the type of fire (exogenous, endogenous). places of origin of combustion centers, its scale, gas situation, number of people captured by the accident and their places of residence, etc. Methodology. During the research, to solve the tasks, the complex used general and special methods, in particular: methods of induction (at the stage of collecting, systematizing and processing information for research) and deduction (in the process of theoretical understanding of the problem), system-analytical , comparative analysis, method of analysis of definitions; economic analysis, possibilities of economic cybernetics and the theory of optimal management in the development of tactics for mining operations, etc. Findings. Economic and mathematical model of rational rescue operations in firefighting differs in that for the first time their management is considered as an economic category, and the process of emergency response and their consequences is presented as an extreme (optimization) problem, which is solved using computational experiments and engineering analysis. An algorithm for solving the extreme problem of optimizing the forces and means of rescue units, based on the fact that the arguments of integral objective functions are not control parameters, but related to the latter determined mathematical model. Methods of calculations in mining, including those used to ensure optimal organization of rescue operations, need to be improved to improve accuracy and simplify their algorithmization in order to reduce the share of manual calculations in mathematical models. Originality. For the first time, on the basis of general methodical provisions of the theory of optimal management integrated quality criteria and on their basis economic and mathematical model of rational conducting of rescue works on liquidation of difficult underground fires are developed. Practical implications. Economic and mathematical model of rational rescue operations will allow timely and correct selection of methods, forces and means of fire fighting in coal mines, minimize economic losses, increase the efficiency and safety of emergency response. Keywords: accident, coal mine, mining works, integrated quality criteria, fire, economic-mathematical model.