The compulsory contractual liability insurance for damage caused by motor vehicle is the most sold in non-life insurance. Nevertheless, many cars are uninsured in Slovakia. The aim of our bachelor thesis is to describe the causes of this phenomenon, analyse the situation and propose solutions to achieve the minimum number of defaulters, alternatively zero number of defaulters. The first part will focus on theoretical definition of the insurance industry, the insurance market and the market with compulsory contractual insurance. In the second chapter we will analyse the problem with non-payers in compulsory contractual insurance. In the last chapter, we evaluate the information obtained and suggest possible solutions to this problem.