This article explores the impact of the crisis on Ukraine's insurance market, identifying the most significant challenges for its financial and economic security in modern conditions to justify the theoretical approaches to crisis management of insurance activities and practical aspects of anti-crisis measures for the insurance market of Ukraine. In our opinion, it is advisable to separately define the concept "crisis management of insurance companies", which combines both measures of organizational and financial management, that managers implement directly within individual insurers, and authorized actions of regulators and insurance supervisors in the crisis, aimed at managing the totality of the insurance market subjects that allow insurers to exit the crisis period at low cost and guarantee the protection of the policyholders (insured) interests. Crisis regulation of insurance activity carried out at different levels of the economic system (macro, micro) and at all stages of its development: in standard conditions; in the pre-crisis situation; during the crisis; during the post-crisis development. In the article crisis management measures for insurance market are classified considering levels and stages of the economic system development. The author outlines the directions of the Ukraine's insurance market restructuring, necessary for survival in times of crisis and further development, and determines features of crisis management measures at the micro level - in insurance companies. Crisis situation is a unique opportunity to focus on business processes, quality, speed and convenience. In addition, this is time to prepare the foundation for future growth. Managers of insurance companies should focus on it now - teach sellers to be more active, keep the existing customer base as efficiently as possible, including the use of new technologies, services and IT in the first place. Strategically anti-crisis activities should be preventive. Protective anti-crisis programs must become an integral part of the financial management of the insurance company.