The paper has identified the essence of the stress testing of the insurance company according to results of the morphological analysis. There was developed the classification of methods of stress testing for insurers used in national and international practice. Main risks of insurance companies’ activities were analyzed. The authors identified, that the main risks of insurance companies are insurance, market, credit and operational. Examples of stress scenarios for the main types of risks of insurance companies were presented. The authors identified the main requirements of the Directive of EU Solvency II, the Standards and Principles of the International Association of Insurance Supervisors in stress testing of insurers. There were developed recommendations to the adaptation of European requirements in stress testing of insurance companies on the insurance market of Ukraine. The economic–mathematical model of stress testing of the insurance risk impact on the activities of the insurance company was developed.