A postbuckling analysis procedure for simply-supported, symmetrically laminated, rectangular, generally orthotropic plates under uniaxial compression based on a Marguerre-type energy method was developed. The analysis assumes the out-of-plane displacement to be represented by using a truncated Fourier sine series. The unknown coefficients of the displacement function were obtained from a system of nonlinear algebraic equations by using the principle of minimum potential energy. The number of terms that are to be retained in the out-of-plane displacement function to obtain an accurate response was studied and identified for a wide range of generally orthotropic plates. In the postbuckling load range, plates are also allowed to change their buckled form. The magnitudes of the total potential energy for possible different deformed shapes of a plate were compared to determine the actual deformed shape. The effect of bending-twisting coupling terms on the postbuckling behavior of anisotropic laminates was also investigated. Several postbuckling problems for isotropic, orthotropic, and anisotropic plates were considered and the results obtained by the present approach were compared with available literature results and finite element solutions to demonstrate the present analysis procedure. The analysis procedure developed was, then, applied to minimum-weight design of laminated plates for postbuckling performance. Laminate failure load used in the postbuckling regime was calculated based on a maximum strain failure criterion. The failure criterion was demonstrated to predict the failure load reasonably well when compared with available test results. Weight comparison between the plates designed against buckling and the ones designed for the postbuckling strength was made to quantitatively evaluate the weight savings achieved for plates that are allowed to buckle. The design variables were assumed to be the layer thicknesses with specified fiber orientations and assumed to take only discrete values. A simple approach based on the penalty method was proposed to achieve the discrete-valued designs. In addition to the regular penalty terms for constraint violation, the proposed approach introduces penalty terms to reflect the requirement that the design variables take discrete values. A variable magnitude penalty term in the form of a sine function was implemented with the extended interior penalty method of the optimization package NEWSUMT-A. The proposed discrete optimization technique was applied to the classical truss and laminated composite plate design problems to demonstrate the performance of the procedure. / Ph. D.