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The paper shows the inevitability of technological mode shift driven by the Industry 4.0, which implies the ubiquitous implementation of information technology, total automation of various processes and creation of cyber-physical systems with artificial intelligence. This requires a complete restructuring of manufacturing systems and production relations, especially in the economies of those countries that want to take a decent place in the new international division of labour of the digital future. An analysis of the world experience of such changes connected with smart industrialization, digital transformations of the economy, the emergence of the industrial Internet of Things and big data processing made it possible to draw the conclusion that it is necessary to apply economic and mathematical methods to justify the expediency of such transformations: economic validity, as well as physical viability of newly created systems. The use of the apparatus of economic and mathematical modeling allows studying properties of the smart system that is being designed, evaluating its effectiveness and risks, anticipating the emergence of problems and errors - without the risk of incurring significant losses which is inevitable when making direct changes in the object of research. Therefore, the purpose of this paper is to study the world experience in the economic and mathematical modeling of smart enterprises and to substantiate its use in the conditions of Ukraine. The review of publications, reflecting the aspects of economic and mathematical modeling in these areas, allowed to conclude that the methodical and methodological apparatus for modeling these processes is unsystematic and inefficient, as well as to formulate recommendations on the economic and mathematical modeling of smart enterprises in Ukraine. In order to take into account the specific features of Ukraine's technological and institutional development, a number of economic and mathematical modeling tools based on the use of production functions, models of inter-branch balance, network optimization models and simulation models based on stochastic dependencies were offered to support the creation of smart enterprises. [ABSTRACT FROM AUTHOR]