The analysis of slope earthquake stability is one of the most important research subjects in geotechnical engineering and earthquake engineering.Two different concepts of slope earthquake stability are put forward:strength reserve stability and dynamic overloading stability.The first concept of slope earthquake stability has been widely accepted,and relative analysis methods are also well de-veloped;the second one,however,is seldom mentioned until now,and the failure criterion and the analysis method based on this concept are yet to be explored.What are researched are just the failure criterion and the analysis method of dynamic overloading earthquake stability.The criterion of critical earthquake peak acceleration for the dynamic overloading stability of a slope and its analysis method,the load increasing method(LIM),are put forward.The dynamic overloading earthquake stability of a loess slope at Changshougou(长寿沟) in Baoji(宝鸡) City,Shaanxi(陕西) Province,China,is analyzed with LIM.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 of 10% in the next 50 years. The analysis of slope earthquake stability is one of the most important research subjects in geotechnical engineering and earthquake engineering. Two different concepts of slope earthquake stability are forward: strength reserve stability and dynamic overloading stability. The first concept of slope earthquake stability has been a accepted, and relative analysis methods are also well de-veloped; the second one, however, is seldom mentioned until now, and the failure criterion and the analysis method based on this concept are yet to be explored. What are researched are just the failure criterion and the analysis method of dynamic overloading earthquake stability. the criterion of critical earthquake peak acceleration for the dynamic overloading stability of a slope and its analysis method, the load increasing method (LIM), are put forward. dynamic overloading earthquake stability of a loess slope at Changshougou (in Baoji) City, Shaanxi (Shaanxi) Province, China, analyzed with LIM. 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 of 10% in the next 50 years.