Abstract In this study a newly developed thin-walled structure with the combination of circular and square sections is investigated in term of crashworthiness. The results of the experimental tests are utilized to validate the Abaqus/ExplicitTM finite element simulations and analysis of the crush phenomenon. Three polynomial meta-models based on the evolved group method of data handling (GMDH) neural networks are employed to simply represent the specific energy absorption (SEA), the initial peak crushing load (P1) and the secondary peak crushing load (P2) with respect to the geometrical variables. The training and testing data are extracted from the finite element analysis. The modified genetic algorithm NSGA-II, is used in multi-objective optimisation of the specific energy absorption, primary and secondary peak crushing load according to the geometrical variables. Finally, in each optimisation process, the optimal section energy absorptions are compared with the results of the finite element analysis. The nearest to ideal point and TOPSIS optimisation methods are applied to choose the optimal points.