The availability of transplant medicine in individual countries is influenced by several factors, among which one should mention, for example, the death rate in road accidents, the amount of the Gross Domestic Product per capita, the amount transferred to the health service, the general public attitude to this method of treatment, the adopted legislation, in particular the model of giving consent to post-mortem organ donation, the number of active transplant centers and active transplant coordinators, and statistics on the conduct of procedures with the participation of living donors. Unfortunately, attempts made to increase the availability of transplant material so far have not led to a visible shortening of waiting lists. The global, chronic shortage of organs, tissues, and cells that could be transplanted forces us to look for new solutions to reduce the list of patients waiting for transplantation. In this paper, the author considers whether an increase in the pool of available transplants could occur due to the introduction of priority rules in the organ allocation procedure.