Even with the advent of efficient, faster computers, researchers are often forced to scale down some of their problems, or pay a high price on huge computer resources for solving them. This has led to an intense effort directed towards developing efficient and rapid analysis procedures. This scenario is also true for many research-oriented finite element codes which have a limited element library or have a problem-size limit because of the use of a memory-resident equation solver. This study focuses on the development of a simple and accurate global/local method for calculating the static response of simply-supported, laminated composite panels, with cutouts and cracks. The approach primarily involves two steps. In the first step a global approach, the Rayleigh-Ritz method, is used to calculate the response of the structure. Displacement based Ritz functions for the plate without the cutout are augmented with a perturbation function. which is accurate for uniform thickness isotropic plates only, to account for the cutout. The Ritz solution does not accurately satisfy the natural boundary conditions at the cutout boundary. Therefore, a second step, local in nature is taken in which a small area in the vicinity of the hole and encompassing other points of singularities is discretized using a fine finite element mesh. The displacement boundary conditions for the local region are obtained from the global Ritz analysis. The chosen perturbation function is reliable only for circular cutout in uniform plates, therefore elliptical cutouts were suitably transformed to circular shapes using conformal mapping. Cracks are modeled as elliptical cutouts with high aspect ratios. The methodology is also extended to the analysis of composite plates. Composite structures have very high structural efficiency due to the high values of stiffness and fiber strength. But the design and analysis of composite structures is much more complicated than that of metallic structures because of the presence of highly directional properties which induces anisotropy in the mechanical characteristics and lead to a myriad of failure modes. Behavior of these structures in the presence of various discontinuities, particularly cutouts and cracks. could be even more complicated. Global/local analysis of composites with cracks and cutouts proved to be very useful and more efficient. The proposed approach resulted in considerable savings in both computational times and data storage without sacrificing the accuracy in the prediction of stresses. Results are compared with adaptive meshing technique, and it is seen that global/local analysis performed equally well. The method is very useful in design and optimization where a large number of analyses have to be performed. / Ph. D.