This paper presents a mathematical and mechanic model for non-linear dynamicstability analysis of structures on the basis of Liapunov's stability criteria. Due to the complexityand difficulty in numerical calculation,a matrix function to this type of stability problems is selectedand the programing formulations are derived.Applying the method to beam or frame structures un-der the axial period loadings,the geometric non-linear dynamic stability results are obtained.Fromthe results,the basic characteristics of this type of probtems,especially the non-linear effect areshown.The model and matrix function method are valtiable both in theory and in practice for struc-tural non-linear dynamic stability.