Optimum structures must have adequate resistance against external random loads. Since most truss structures involve a series of failure processes, it is necessary to develop system reliability analyses for the optimum design of truss structures. In this paper, a hybrid method of system reliability-based design optimisation (SRBDO) is proposed by combining genetic algorithms (GAs) and radial basis functions (RBFs) neural networks. The proposed method is applied to truss structures, and then the validity is demonstrated through two specific examples. Detailed discussions for the failure sequences such as buckling failure and bending failure are presented. It is concluded that the structural weight increases significantly with the increase of the target 52 Y. Liu et al.system reliability index or the coefficient of variation of design parameters. Results of two optimisation schemes of the steel truss girder show that the cross-sectional areas of the beams are decreased and those of web members are increased.Reference to this paper should be made as follows: Liu, Y., Lu, N., Noori, M. and Yin, X. (2014) 'System reliability-based optimisation for truss structures using genetic algorithm and neural network', Int.