Risk analysis can overcome the weakness of conventional safety evaluation of high-arch dams where the random nature of the load and resistance effect are ignored and the failure mode and failure disaster loss are not taken into account. On the basis of statistical analysis of the data of the failure arch dams and faulty and perilous arch dams in the world, it is deduced that the failure of high arch dam is mainly caused by super elevation floods, highly intense earthquakes, mountain landslides, abnormal temperature variation, explosion load, etc. Five major failure modes for high arch dams are suggested, namely dam abutment rock instability, fundamental plane instability, entire entity instability, excess cracking and extreme dam overflow. Based on the study of the failure mechanism of the major failure modes, a state function is established to calculate the failure probability of the major failure modes. An approach is developed to obtain the statistical quantity and the regularities of distribution of the load and resistance random variables.