The shadow economy at the transitional stage of development of Ukraine became an integral part of the economy, began to solve a number of macro and microeconomic problems of the state. Today, the shadow economy has a significant impact on all socio-economic processes occurring in the country. But the shadow economy’s share of gross domestic product today is so large that it poses a threat to national security. A significant level of the shadow economy leads to the criminalization of society, the growth of corruption, the formation of an atmosphere of legal nihilism in the state. Tendency to evade taxes causes significant damage to Ukraine’s budget. This, in turn, narrows the transition to a welfare state model, as it reduces resources for infrastructural upgrades, social payments, medical and other social services for the population. Official estimates of the size of the shadow economy by various government agencies have considerable differences. Inaccurate assessment of the impact of the shadow economy on all spheres of the country’s activity leads to irrelevant assessments of socio-economic processes and their tendencies, miscalculations in the formation of domestic and foreign policy of Ukraine. The shadow economy has been researched by many scholars, but in the considerable number of works on this topic there are no even well-grounded data on the shadow economy. Therefore, the urgent task is to develop an algorithm for estimating the shadow economy. To do this, the article analyzes various terminological approaches to defining the shadow economy and its components. The classification of existing methodological approaches to the identification and assessment of the extent of shadow economic activity is carried out. A mathematically correct method of estimating the size of the shadow economy which is suitable for practical use has been proposed and substantiated. The analysis of the obtained mathematical equation showed that it is possible to formulate mathematically precisely the conditions for a stable level of the shadow economy and the growth of the shadow economy. The estimation of the correlation functional of the shadow economy size became mathematically accurate.