Abstract: In order to develop national and civil economy, make full use of water resources and hydropower resources, more than a dozen of over 200 meter-high and even 300-meter high arch dams are being building and will be built in China, both whose scale and difficulties of construction are the greatest in the world, and many challenging scientific and technological problems come along as well. Most of these high arch dams are built in western alpine and gorge region where topographic and geologic conditions are very complex, with bad environment and high seismic intensity. All these threaten safety of high arch dams seriously. Thus, failure mechanism and safety assessment of high arch dam under disaster conditions has always been a highly concerned issue to dam experts. The global failure mechanism and analysis methods of high arch dam accordingly are the main content of safety research for arch dam, however, there is no uniform understanding of mechanics mechanism of global failure and feasible methods based on mechanics theory. In this paper the current safety assessment methods are introduced briefly and the open problems are pointed out. According to stability theory of a mechanics system, it is demonstrated that the essence of the global failure of a high arch dam is stability issue. According to the features of the load-displacement curve in its failure progress, failure of a high arch dam belongs to the physical instability problem caused by non-linear material, started in local strength damage, which is the extreme point destabilization. Some analysis methods of the global stability for a high arch dam are presented, in which the Indirect Method based on elastic-plastic progressive analysis is considered to be a feasible method at the present time to study the global stability of the high arch dam, which is verified by physical model test. However, the Indirect Method is not derived directly from stability theory of a mechanics system, and the scientific analysis method and the destabilization criterion should be obtained from the physical disturbance equations. And the effect of the non-linearity on the ultimate bearing capability (UBC) of a high arch dam is shown, the perfect elastic-plastic constitutive relationship and geometric non-linearity make the capability to be overestimated, which is unsafe. Moreover, to determine the UBC of a dam, the criterion based on maximum elastic strain energy and the condition based on mutation theory are presented.