Thin-walled columns play an important role on passenger safety in vehicular collisions for their progressive deformation patterns and large energy absorptions. A thin-walled column is often desirable to the automotive industry, because such designs could enhance safety and reduce manufacturing cost. Due to the complexity of crash mechanism, obtaining such designs has been a challenge to the trial-and-error approach using physical prototype testing. To this end, combining finite element simulations with optimization methodologies has become the viable means to meet the challenge In this thesis, a numerical study of crushing of tapered octagonal tubes was carried out to investigate their behaviors under axial impact loading. To simulate this behavior the software code ABAQUS/Explicit 6.9 was used and FE models were constructed to study the characteristics of the tubes. The crash performances of the tubes are evaluated by three criterions: The mean crushing force, the crush force efficiency (CFE, the ratio of the average crushing load to the peak load), and the specific energy absorption (SEA, absorbed energy per unit mass). Parametric studies were conducted to determine the effect of geometrical parameters such as the axial length of tube, the side length, the taper angle and the tube thickness on crushing behavior of the tapered tubes. The FE results are then compared with the existing solution as well as the available experimental data which are shown to be in good agreement. Then theoretical models for predicting the mean loads in the plastic post-buckling range were developed on the basis of inextensible and extensible folding mechanism based on the stationary and travelling plastic hinges. The analytical results were compared with simulation ones and is shown to be in good agreements. In addition, the optimum values of geometrical parameters are sought for maximum CFE and maximum SEA using surrogate based optimization. Multi-objective genetic algorithms (GAs) are used for Pareto-approach optimization of the energy absorption of the tubes. The design of experiments (DoE) of the factorial design is employed to construct surrogate models for the objective of specific energy absorption ( SEA ) and the crush force efficiency (CFE). Response surface, artificial neural network and GMDH are the different surrogate models used in this study and The Non-dominated Sorting Genetic Algorithm –II (NSGAII) is applied to obtain the Pareto optimal solutions and as a result, a set of Pareto optimal solutions for every method are visualized. It is noted from the Pareto optima that these two objectives strongly compete with each other and different criteria are emphasized along the Pareto frontier. Based on this optimization procedure, the optimum tube size for crashworthiness in the impact loading condition has been presented in the three aims. These aims covered in objective functions with different weighting factors. It is detected that the maximum CFE requires relatively large thickness, and large taper angle, while the maximum SEA requires large thickness and small taper angle. Although ANN was found to be the most accurate surrogate model for SEA and CFE prediction but it was also detected that the globally most accurate surrogate model does not necessarily lead to the optimum. Keywords Tapered tubes, Axial Crushing, Crush force efficiency, Specific energy absorption, Multi-objective genetic algorithms, Pareto-approach optimization, Response surface, Artificial Neural network