Blockchain technology has developed significantly over the last decade. One of the reasons for this is its sustainability architecture, which does not allow modification of the history of committed transactions. That means that developers should consider blockchain vulnerabilities and eliminate them before the deployment of the system. In this paper, we demonstrate a statistical model checking approach for the verification of blockchain systems on three real-world attack scenarios. We build and verify models of DNS attack, double-spending with memory pool flooding, and consensus delay scenario. After that, we analyze experimental results and propose solutions to avoid these kinds of attacks.