The integrity assessment of reactor pressure vessel (RPV) often considers only the crack initiation to evaluate the safety margin and excludes the crack propagation analysis. In this contribution, the combined eXtended Finite Element (XFEM) method with the Initiation-Growth-Arrest (IGA) algorithm, shortly written as XFEM-IGA, is applied to a thick-walled cylindrical specimen with a circumferential crack under Pressurized Thermal Shock (PTS). The results of the crack propagation analysis are compared with the experimental ones to validate the approach, which were taken from large-scale experiments on thick-walled cylinders under PTS performed in the FALSIRE project. In order to simulate the cylinder with the XFEM-IGA approach, a reduced three dimensional finite element (FE) model of a small sector (a slice of the cylinder) is used by applying cyclic symmetry boundary conditions. Thus, the model profits from the cyclic symmetry not only of the cylinder geometry but also the circumferential crack. The closed-form for the stress intensity factor for an internal circumferential crack in a thick-walled cylinder is combined with the IGA algorithm and is presented to verify the quality of the results. The results are shown in terms of the SIF evolution and crack depth during the PTS transient. The crack depth shows several initiation-arrest-reinitiation cycles and final arrest. However, some differences in the number of these cycles and final crack depth are observed between the simulation and the experimental results.