Many varied methods exist for the derivation of optimum aerofoil shapes by the combined use of numerical optimisation techniques (optimisers) and Computational Fluid Dynamics (CFD). Some are capable of optimisation at more than one design point (multi-point design). This Data Item deals with the principles of the technique in general and, for illustration, the application of one such multi-point method (CODAS) in particular. The Data Item gives an overall view of the optimisation design method and presents a general description of the constrained multivariate optimisation process. It also deals with some aspects of geometry definition and discusses the CFD methods involved. A brief survey of current optimisation methods is given in an Appendix.