In a nuclear power plant, the integrity of the pressure vessel which contains the primary water is paramount. In case of an accident involving the guillotine break of primary system piping there can be a sudden loss-of-coolant accident (LOCA). During such an incident, the reactor core needs to be cooled for some period after its shut-down (residual heat removal). The emergency core cooling is achieved by the injection of cold water in the still pressurized reactor pressure vessel (RPV). The combination of pressure and thermal stresses provides a complex stress state in the RPV wall: a pressurized thermal shock (PTS). The RPV material is generally a ferritic steel. The critical stress intensity for brittle cleavage fracture depends on the ductile to brittle transition temperature. This complex combination of stresses, absolute temperatures and temperature gradients in combination with radiation damage requires an integral approach for the evaluation of the probability for the occurrence of cleavage fracture. This problem is simulated with a combined CFD and FEM approach. A quarter of the reactor pressure wall including the cooling nozzle is simulated during the 1000 seconds of the cooling transient. This method can accurately predict the thermal profile and the corresponding stress field. This approach is applied to a reactor pressure vessel containing pre-existing semi-elliptical cracks. The stress intensities for every time step, the temperature, the effects of radiation damage, and the material properties of two types of RPV steel; (SA-508gr.3 and SA-508gr.4N) contribute to the probability for a brittle cleavage crack to form. An estimation of the probability for cleavage fracture is made through the Master Curve approach. These probabilities are calculated for different crack locations, sizes, aspect ratios and for two different grades of RPV steel. The influence of these geometric factors and material properties under the influence of radiation have been analysed. The material just below the nozzle is cooled down further and the thermal gradient is more severe. This is reflected in a higher probability for cleavage fracture. The new generation of RPV steel; SA-508gr.4N is very promising for its resistance to radiation induced embrittlement and for its higher strength, both factors leading to a lower probability of cleavage fracture in the reactor pressure vessel. Increasing the safety of the RPV.