A methodology to design symmetrically laminated fibre-reinforced structures under transverse loads for minimum weight, with manufacturing uncertainty in the ply angle, is described. The ply angle and the ply thickness are the design variables, and the Tsai-Wu failure criteria is the design constraint implemented. It is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal, and thus the approach is a worst-case scenario approach. The finite element method, based on Mindlin plate and shell theory, is implemented, and thus effects like bending-twisting coupling are accounted for. The Golden Section method is used as the search algorithm, but the methodology is flexible enough to allow any appropriate finite element formulation, search algorithm and failure criterion to be substituted. In order to demonstrate the procedure, laminated plates with varying aspect ratios and boundary conditions are optimally designed and compared.