This thesis investigates the buckling and post-buckling behaviours of varied thickness distribution rectangular plates with three sides simply supported, one longitudinal edge free and a stress gradient applied to the two short edges. The primary aim of this thesis is to provide a design method for the thickness distribution of a plate that meets a design target for buckling behaviours. The main conclusion of this thesis is that a modified evolutionary structural optimisation (ESO) method satisfied the requirements of the design method and successfully controlled the buckling shape and buckling load of the plate. The plates with optimised thickness presented post-buckling behaviours with features according to their buckling behaviours. This research enriches the study of plate buckling with non-uniform thickness from the perspective of the shape of deformations of the plates. The results have potential economic and environmental value to the users and the building and construction industry. The project involved an optimisation of the thickness distribution of a plate for the design target, where in the modified ESO method iteratively redistributed the thickness of the plate. A numerical investigation was adopted to verify that the post-buckling behaviour of optimised plates matched the buckling features of the plates. Experiments were also conducted to verify the post-buckling behaviours of the optimised plates. A numerical simulation of the experiments was employed to predict and limit the differences between the results of the experiment and the simulation. A potential application of the optimised plate as a kinetic façade component was explored. A discussion on the different optimisation algorithms for plate buckling optimisation was presented.