The optimum structural design of the hull girder is discussed in this chapter. In the first part, early efforts at optimisation are described: structural optimisation, topology and scantlings optimisation and nonlinear programming. The use of linear and sequential linear programming and its use in the MAESTRO program are described. The need to consider wider issues is discussed and the various single-parameter optimisation criteria described (design for X). Multi-objective optimisation criteria and Pareto optimality are discussed. The background to genetic algorithms and the fundamental theorem of genetic algorithms are presented. Single and multi-objective optimisation using genetic algorithms is described and illustrated with application to a catamaran structure. The analytic hierarchy process used in the ranking of different criteria put forward by stakeholders in an optimum structural design problem is described. This is applied in a case study described in the last part of the chapter that concerns the optimum structural design of a RoPax carrier. In this finite element models are used in the concept design stage to select a topology of the structure as well as the preliminary design stage. A series of criteria selected by a number of stakeholders are used as a basis for the optimisation process.