New numerical results are generated for compressive biaxial buckling which serve to quantify the effect of boundary conditions on buckling loading. It is observed that, for all cases the buckling load increases with the mode number but at different rates depending on whether the plate is simply supported, clamped or clamped ¿ simply supported. The buckling load is a minimum when the plate is simply supported and a maximum when the plate is clamped. Because of the rigidity of clamped boundary condition, the buckling load is higher than in simply supported boundary condition. It is also observed that as the mode number increases, the plate needs additional support. The aim of the present textbook was to review the importance of studying buckling of composite laminated rectangular plates from the point of view of introduction and basic definitions, the formulation of mathematical modelling of rectangular laminates, the numerical method for predicting the buckling loads and shape modes of buckling of laminated rectangular plates, studying the effect of boundary conditions on buckling loads, and finally the important results and findings of the present study.