In the context of the crisis in Ukraine, it is important to increase the competitiveness of the insurance sector as a measure of its stability and dynamism under various scenarios of economic development. The purpose of this paper is to assess the competitiveness of the insurance sector and determine the impact on its level of factors caused by economic crises. Using the method of integrated analysis, the index of competitiveness of the insurance industry is built, which considers the number of businesses, employment, sales, capital investment in the industry, insurance sector performance, share of profitable enterprises, and profitability of the insurance sector in Ukraine for 2012–2020. The results showed that the impact of the 2014–2015 crisis due to endogenous factors, namely political instability in the country and the devaluation of the hryvnia, led to a significant reduction in the competitiveness index of the insurance sector. At the same time, during the pandemic, the insurance sector is stabilized, as evidenced by the growth of sales and the share of profitable enterprises, as well as increasing profitability of insurance activities. The competitiveness index did not change significantly during the pandemic. To analyze the dependence of the integrated indicator of the competitiveness of the insurance sector on economic fluctuations during the crisis, regression equations are constructed. It is proved that the greatest impact on the competitiveness index of the insurance sector in times of crisis is exerted by changes in employment and the amount of capital investment.