Introduction. Under current conditions of the world economy development the destructive effect of external and internal factors on the activities of economic entities in the financial and real sectors leads to the systemic crises, the consequences liquidation of which requires significant financial and time expenses. Therefore, it may be noted that the functioning of the global economic system demands forming the effective mechanism to prevent and minimize various risks. So, the progressive international tendencies of national economics lead to the consideration of the mechanism, which allows, not disrupting the entrepreneurship market, to neutralize the negative consequences of adverse events on the base of reinsurance market. Purpose. The article is aimed on the methodological principles research of formalization the stability achievement process of the reinsurance market on the theoretical aspects of this issue. Methods. Methodological basis of the articles are fundamental tendencies of the finance and insurance theory, developments of domestic and foreign scientists in the context of problems of the insurance and reinsurance markets functioning, modern insurance management concepts, as well as scientific works of economists, concerning conditions ensure stabilization of the economy. Results. The article is stressed on the essential characteristics and mathematical formalization of reinsurance market stability as a dynamic process of the stable distribution formation between two sets of subjects of this market: the subjects, which transfer risk for reinsurance and the subjects which take risk for reinsurance. The practical implementation of the proposed approach is carried out with the usage of Gale – Shapley algorithm (“algorithm pending approval”), adjusted to the peculiarities of reinsurance market functioning. The stable distribution determines the conclusion and compliance with the conditions of reinsurance contracts between the subjects pairs at the reinsurance market, that is the conclusion of agreements, which can provide: cover of losses in full; implementation of insurance payments or the obligations execution within permissible limits; optimizing the profitability of insurers and reinsurers due to the compromise solution in the context of the tariff rate and the insurance reserves. Conclusion. Thus, Methodological Principles and Formalization of the Stability Achievement Process of the Reinsurance Market allows to define the stability of the reinsurance market, explore its stable distribution on the basis of Gale-Shapley algorithm («algorithm pending approval»), identify the main principles of its formation, realize its practical implementation on the Sample. The stable distribution provide the following key aspects: full covering of losses, making insurance payments or performance of obligations within permissible limits; optimizing the profitability of insurers and reinsurers due to the compromise decision. У статті розглядаються основні характеристики та математична формалізація стабільності ринку перестрахування як динамічного процесу формування стійкого розподілу між двома множинами суб'єктів цього ринку: суб'єктами, що передають ризики у перестрахування і суб'єктами, що приймають ризик на перестрахування. Практична реалізація запропонованого підходу здійснюється з використанням алгоритму Гейла - Шеплі («алгоритму відкладеного узгодження»), з урахуванням особливостей функціонування ринку перестрахування.