This paper presents a formulation of Genetic Algorithm based optimisation for the design of plane and space truss structures with geometrically non-linear behaviour. The cross-sectional areas of truss members are treated as design variables and constraints are imposed on stress, displacement and member instability. Areas of the member are grouped in order to reduce the number of independent design variables and to produce practical designs. An incremental load approach with a Newton- Raphson type of iteration is used in the geometrically non-linear analysis procedure and in developing the optimisation algorithm. A number of design examples are presented to illustrate the application of the proposed algorithm to plane and space truss structures with a large number of design variables. Solving these examples proved that the proposed formulation is viable and leads to optimum solutions. © 2003, Civil-Comp Ltd.