In this study, a computational model for accurate analysis of composite laminates and laminates with including delaminated interfaces is developed. An accurate prediction of stress distributions, including interlaminar stresses, is obtained by using the Generalized Laminate Plate Theory of Reddy in which layer-wise linear approximation of the displacements through the thickness is used. Analytical, as well as finite-element solutions of the theory, are developed for bending and vibrations of laminated composite plates for the linear theory. Geometrical nonlinearity, including buckling and post-buckling are included and used to perform stress analysis of laminated plates. A general two-dimensional theory of laminated cylindrical shells is also developed in this study. Geometrical nonlinearity and transverse compressibility are included. Delaminations between layers of composite plates are modeled by jump discontinuity conditions at the interfaces. The theory includes multiple delaminations through the thickness. Geometric nonlinearity is included to capture layer buckling. The strain energy release rate distribution along the boundary of delaminations is computed by a novel algorithm. The computational models presented herein are accurate for global behavior and particularly appropriate for the study of local effects.