Based on the sense of Liapunov dynamic stability and the features of elastic buckling of arch bridge, and using the static buckling eigenvalue as well as linear time history analysis result, a simplified method for evaluating the elastic dynamic instability was developed from the so called “dynamic eigenvalue method” that needs to extract the minimum buckling eigenvalues step by step under the whole earthquake excitation. The presented method was compared and validated to be efficient and accurate via a case study, and therefore it could be used as a more effective method to study the dynamic stability issue of long span arch bridges and other civil engineering structures.