Abstract: The analysis of earthquake stability of slopes is one of the most important research subjects in geotechnical engineering and earthquake engineering. Two different concepts of slope earthquake stability are put forward in this paper. One concept is the so-called strength reserve stability which can be figured out by comparison of present strength of a slope to its critical strength that is degenerated from its present strength till to the dynamic failure of the slope under the earthquake action of a certain intensity. The other is named as the dynamic overloading stability which can be evaluated by contrast between the actual earthquake action that just makes a slope damaged and the earthquake action as the local antiseismic precautionary standard. The first concept of slope earthquake stability has been widely accepted. Its relative analysis methods are also well developed. The second one, however, is seldom mentioned till now. Its failure criterion and analysis method are yet to be explored. This paper investigates the failure criterion and the analysis method of dynamic overloading earthquake stability. The criteria of the critical earthquake peak acceleration for the dynamic overloading stability of a slope and its analysis method, and the load increasing method are put forward. During the analysis process, the action of earthquake force begins from a lower level and gradually increases to the critical intensity that just makes the current strength slope reach the state of dynamic failure. The earthquake stability of the slope is determined by the comparison of the critical earthquake peak acceleration and the antiseismic precautionary earthquake peak acceleration on the field of the slope. The dynamic overloading earthquake stability of a loess slope at Panlongyuan in Baoji, Shaanxi Province, China is analyzed with the load increasing method proposed in this paper. The analysis result reveals that the dynamic overloading earthquake stability of the slope is quite high to the action of the earthquake ground motion with exceeding probability 10%in coming 50 years.