According to Polish nuclear law, newly emerging nuclear facilities require probabilistic safety assessment (PSA). This article is intended to present the PSA method and to present the error tree method by which the probability of unavailability of the gravity reactor cooling system (GDCS) of the ESBWR power plant designed by GE Hitachi was determined. This work includes creatiion process of a damage tree and performing a quantitative analysis in SAPHIRE tool and estimating uncertainty using the Monte Carlo method. As a part of the work, it was shown that in the probability of failure of a single GDCS P LINE-A line, the most important element are the basic events related in particular to the operation of service valves