Mandatory motor third party liability insurance regulates those relations on the basis of which the injured parties are provided with compensation for damage. Already at the moment when the first motor vehicle appeared, which by its very use led to the first traffic accidents, the idea began to develop in all countries of the world to legally regulate the issue of liability of owners or users of motor vehicles for damages suffered by third parties. The first method that appeared as insurance against damage caused by traffic accidents appeared in the form of voluntary insurance. However, it quickly became clear that voluntary insurance did not provide satisfactory protection to third parties injured, and the number of accidents became higher and higher every day, and the question arose as to how to achieve better protection of those injured in accidents. Thus, the idea to introduce the obligatory conclusion of a contract on motor liability insurance arose very quickly, all with the aim of better protection of injured persons. Over time, it was concluded that liability insurance for owners or users of motor vehicles for damage caused by the use of motor vehicles to third parties is inevitable and that it is the best way to protect victims of traffic accidents. The protection of injured persons is achieved through the procedure of compensation for damage that should be fast and effective, and able to bring the injured persons back into the normal life of the community. For this purpose, the paper deals with the issue of protection of third injured parties with compulsory motor third party liability insurance, and presents all the problems and challenges faced by third injured parties in exercising the right to compensation as a fundamental obligation under motor liability insurance contracts. The paper underlines certain means of protection of the injured party that the legislation introduces in order to facilitate and simplify the procedure of compensation for damages and thus enable the injured parties to obtain full compensation for damage in a fast and efficient manner.