In this article, practical issues are considered at the complex level, in the field of realizing mathematical modelling of the assessment of the potential of the Ukrainian IT industry in the conditions of global challenges. The purpose of the study is to analyze modern approaches to evaluating this potential using advanced mathematical methods, such as multifactorial regression, cluster analysis and factor analysis. The work describes in detail the methods that allow you to evaluate the relationships between the main economic, technological and social indicators that influence the globalized development of the modern IT sector in Ukraine. The study emphasizes the strategic importance of assessing the capabilities of the IT sector to solve modern economic and technological tasks. Within mathematical modeling in the work, an improved model of evaluation of the above potential is proposed in which the combination of considered methods with the combination of the principles of Bayesian data analysis is combined. This approach allows you to more accurately take into account the uncertainty and variability inherent in modern economic and technological conditions. Usage of the Bayesian approach makes it possible to get a more flexible and adaptive model that better reflects dynamic processes that affect the development of IT industry in Ukraine in global challenges. The analysis begins with multifactorial regression, which examines the relationship between economic, technological and infrastructure factors that influence the development of the IT sector. The next stage is a cluster analysis that allows you to distinguish regional IT-hubs, comparing their effectiveness and revealing differences in Ukraine. With the help of factor analysis, we reveal the hidden variables that have a significant impact on the development of the industry. We also compare the results of each of the models to identify common trends and differences, which allows not only to identify opportunities for development, but also to indicate problems that need attention. Based on the results obtained, we offer specific recommendations for improving the competitiveness and stability of the Ukrainian IT industry. Our conclusions emphasize the importance of using innovative approaches to achieve more efficient development of this field.