This paper analyzes the market structure of the Hungarian insurance market, which operated as a monopoly market until 1986. After the regime change this sector started to develop rapidly. But the Hungarian insurance market has a strong oligopolistic character, and thus raises an interesting question as to how close the market is to a state of perfect competition. Based on the Panzar and Rosse (J Ind Econ 35:443–456, 1987) methodology we estimate the elasticity of total revenues with respect to changes in input prices, so that we can determine the market structure. The estimation of input price elasticity is made with a static and a dynamic panel model. According to research the structure of the Hungarian insurance market significantly differs from the perfect competition case between 2010 and 2019. The market is in long-run equilibrium, and the hypothesis of the monopoly case cannot be rejected. The market structure of a sector is important for modelling phenomena and new regulations effectively, which is relevant for insurance and competition supervision in the protection of customers.