The postbuckling load carrying capacity of composite plates offers immense potential to their applications for loads exceeding their primary buckling load. However, such an efficient and economical usage of these plates can be reliable only if the nonlinear postbuckling behavior of these plates, which includes a good understanding of secondary buckling, is understood thoroughly. The present investigation is an attempt to understand secondary buckling of almost square composite clamped-simply supported plates, both unstiffened as well as stiffened, in some detail. With the help of the finite element method, a large number of numerical studies have been conducted to understand the secondary buckling characteristics. The sensitivity of these characteristics to variations in boundary conditions, lamination sequence, imperfections, and stiffener geometry has been considered. It has been found that the occurrence of secondary buckling in clamped-simply supported plates under uniform end shortening critically depends on the intensity of restrictions imposed on the inplane normal displacements along the unloaded simply supported edges of the plate. These restrictions could be due to the actual boundary conditions at these edges, or due to the presence of stiffeners along these edges. It has also been found that the presence of imperfections significantly delays the event of secondary buckling. Finally, it has been found that changes in lamination sequence of the plate alter its secondary buckling characteristics in ways that are, in general, quantitative in nature. The numerical investigations were followed by a limited number of experiments involving the testing of unstiffened as well as stiffened composite plates with the intent of augmenting the confidence in the numerical predictions made. Three different lamination sequences were considered during the testing phase of this investigation. It was found that the agreement between experimental data and numerical predictions was quite good. The occurrence of secondary buckling followed the predictions closely.