Abstract: UN-kernel TRISO particles consist of UN-fuel kernel coated with four layers, including buffer layer, inner high-density pyrocarbon (PyC) layer, SiC layer, and outer highdensity pyrocarbon (OPyC) layer, which have good fission product retention capability under normal operation and severe conditions. The failure probability of TRISO particles is one of the most important design parameters that reflect the safety characteristics of TRISO particles under the conditions of normal operation and severe core heatup accidents. Hence, the theoretical method for evaluating the failure probability of UNkernal TRISO particles was introduced in present work. Firstly, the theoretical model of failure probability for UNkernel TRISO particle was developed on the model based on a pressure vessel model, namely the modified PANAMA model, which included a degradation effect on the SiC layer due to fission product corrosion, the effect of internal gas generated by fission gas release of UN kernel on SiC layer together with the creep and shrinkage of IPyC layer and OPyC layer on SiC layer. The stress model of SiC layer was rebuilt and validated by IAEA benchmark problems, respectively. Furthermore, the conservative models of creep coefficient, the radial and the tangential swelling rate for highdensity pyrocarbon introduced by neutron radiation were introduced. Then the failure probability of UNkernel TRISO particle under extremely severe conditions (1 600 ℃, up to 1 000 EFPD and 30% FIMA) was analyzed by introducing partial random and complete random sampling method. And the Spearman correlation coefficients between the parameters of each layer and the failure probability were also presented. The evaluation results show that the failure probability of UNkernel TRISO particle increases significantly by random sampling method comparing with the former fixed parameter method and a positive correlation exits between the design parameters of buffer layer (such as dimension and density) and failure probability, while a negative correlation exits for those of other layers. Furthermore, the effect of the distribution of the design parameters of each layer for UNkernel TRISO particle, such as the distribution of thickness and density, on failure probability was also conducted with the complete random sampling method. The results show that the design parameters of buffer layer play a dominant role in the evaluation of failure probability of UNkernel TRISO particles, which is followed by those of SiC layer, while the effect of those of IPyC layer and OPyC layer is so small to be ignored. That is, the overall failure probability of UNkernel TRISO particle under severe accident conditions can be controlled by optimizing the design parameters of the buffer layer and SiC layer, for example, reducing the standard deviation of the distribution of the thickness and density. In other words, the optimization of the design parameters of buffer layer and SiC layer can notably improve the safety of UNkernel TRISO particles.