This study is devoted to the proposed approach to the use of information technologies, in particular, computer geometric modeling, to improve the efficiency of management of complex socio-economic systems on the example of modern Orthodoxy. The urgency of the chosen topic is due to the rapid return of a large number of people in our country to eternal Christian values after many years of forced atheism. These facts significantly contribute to the current intensive restoration of religious buildings, the construction of new temples, the revival of monasteries, the improvement of places of pilgrimage, the optimization of proper organizational and territorial church structures, the implementation of spiritual-educational and other charitable activities. Our days are characterized by global social changes, such as the widespread introduction of market relations in all spheres of life, land, medical, educational reform, decentralization of state power and more. The above features reveal the high dynamism in the spiritual and material plan of the current stage of development of Ukraine, which is significantly burdened by the COVID-19 pandemic, the military conflict with Russia and other unfavourable factors. The main purpose of the publication is to highlight the developed mathematical apparatus for the automated reproduction of the organizational-territorial cluster structures of Orthodoxy. This ensures, on the basis of the proposed complex geometric models, the improvement of church governance, for example, regarding the definition of rational territorial boundaries of parishes and dioceses, the determining of the need for their unification, liquidation or the formation of new ones, optimization of the location of temples, chapels, educational institutions, etc. The considered approach allows to save material, financial, human and natural resources, to reduce terms and to improve the quality of acceptance of various decisions. The latter applies to a large number of objects and processes, their various properties. The article also outlines promising directions for further scientific research on the selected topic.