The importance of plates, with discontinuities in boundary supports in aeronautical and marine structures, have led to various techniques to solve plate problems with mixed edge support conditions. The domain decomposition method is one of the most effective of these techniques, providing accurate numerical solutions. This method is used to investigate the vibration and buckling of flat, isotropic, thin and elastic plates with mixed edge support conditions. Two practical approaches have been developed as an extension of the domain decomposition method, namely, the primary-secondary domain (PSD) approach and the line-domains (LD) approach. The PSD approach decomposes a plate into one primary domain and one/two secondary domain(s). The LD approach considers interconnecting boundaries as dominant domains whose basic functions take a higher edge restraint from the neighbouring edges. Convergence and comparison studies are carried out on a number of selected rectangular plate cases. Extensive practical plate problems with various shapes, combinations of mixed boundary conditions and different inplane loading conditions have been solved by the PSD and LD approaches. / Master of Engineering (Hons)