The last accidents of the nuclear power plant (NPP) in Chernobyl and Fukushima give us the new inspiration to verify the safety level of the NPP structures. This paper presents the new requirements to test the safety and reliability of the NPP structures due to the recent accidents in the world. The IAEA in Vienna required in the document 'Stress tests' the verification of the safety of the NPP structures under impact of the extreme loads as the earthquakes, the extreme climatic actions and the technology accidents. The new recommendations to load combinations and design criteria were defined. The risk assessment to verify the safety and reliability of the NPP structures based on probabilistic and nonlinear analysis is presented. The uncertainties of material model (behaviour of the reinforcement and liner, concrete cracking and crushing), degradation effects, the loads level (dead and live loads, extreme climatic and accidental temperature and overpressure) as well as other effects following from the inaccuracy of the calculated model and numerical methods were taken into account in the response surface method (RSM) method. The results of the deterministic and probabilistic analysis of the NPP structures are presented.