Throughout history we have witnessed several major breakdowns of the financial system which leads to the question of their causes. Although to the term ”financial system” belongs a variety of intermediaries, to facilitate terminology, this paper discusses the interbank system, which is made up of n banks and their mutual claims to each other. The paper discusses the contagion in financial networks - the probability of occurrence and the extent of its spread, if it occurs. The term contagion is equated with bankruptcy of banks which is transferred from one bank to another. The theoretical part of the model is based on a directed graph and generating functions that generate a probability degree distribution, while the second part of the paper presents results that confirm the theoretical assumptions. The conclusion is that there is a ”window” in which infection breaks out for a certain value of average degree in the graph. Although the system can be resistant to most shocks of particular magnitude, if it is hit by such a shock to a specific place, which may have been structural weakness of the system, the instability of the system can be significant. It turns out that the financial system is robust, but fragile - although the probability of contagion is low, the consequences can be extremely widespread.