In this article, the multi-objective optimization of cylindrical aluminum tubes under axial impact load is presented. The specific absorbed energy and the maximum crushing force are considered as objective functions. The geometric dimensions of tubes including diameter, length and thickness are chosen as design variables. D/t and L/D ratios are constricted in the range of which collapsing of tubes occurs in concertina or diamond mode. The Non-dominated Sorting Genetic Algorithm-II is applied to obtain the Pareto optimal solutions. A back-propagation neural network is constructed as the surrogate model to formulate the mapping between the design variables and the objective functions. The finite element software ABAQUS/Explicit is used to generate the training and test sets for the artificial neural networks. To validate the results of finite element model, several impact tests are carried out using drop hammer testing machine.