In this thesis, a method for seismic analysis of multiply supported secondary structures subjected to nonuniform excitation at each support is developed. The method is the multiple response spectrum method with additional terms for the correlation effects of the support motions. For the purpose of comparison, three conventional methods are employed in this study. They are the single response spectrum, multiple response spectrum, and time history analysis methods. Example analysis has been carried out 5 different structure. The numerical results indicate that the present method yields more accurate results of the maximum response than the conventional response spectrum analysis methods.