Research on optimum lay-ups and buckling loads of laminated plates is briefly reviewed. A new sequential, iterative procedure, known as layerwise optimization (LO), for determining the optimum lay-ups and maximum buckling loads of symmetrically laminated rectangular plates is described. The physical basis of the procedure is explained. LO is shown to be highly efficient, with reductions in computational effort of more than 99 per cent being possible in comparison to some simultaneous optimization procedures. Three examples are presented of the use of the LO procedure to determine the optimum lay-ups and associated maximum buckling loads of 8- and 24-layer symmetrically laminated rectangular plates subjected to uniform, uniaxial and biaxial compression. For 18 combinations of free, simply supported and clamped edge conditions, it is shown that the LO procedure generally leads to the optimum solution. In the very few instances where a local rather than a global solution was obtained, the maximum buckling load was only 4-6.5 per cent lower than the optimum value.