Energy absorbers are widely used in many engineering structures, especially mobile ones to prevent or alleviate the impact damages. Thin-walled structures are employed as an important category of energy-absorbing systems. In this study, the effect of thickness variations in different parts of a particular structure is investigated on the energy absorption behavior. The geometry of the considered structure is a four-cell squared-section of aluminum alloy 6061 that is subjected to the lateral loading and the thicknesses of the sides are defined as the input variables. For the systematic investigation of the input variables effect, design of experiments procedure is utilized. The simulations are performed by the LS-Dyna software using the finite element method based on the output data of design of experiments. Moreover, in order to ensure the accuracy and validity of the simulations, an experimental investigation has been conducted for one of the scenarios and the results are confirmed. According to the results of numerical investigations, it was found that all the input variables of the problem are effective with distinct and considerable trend in energy absorption of the structures. These trends are generally nonlinear and relative extremum can be observed in some of them. Finally, by analyzing the energy absorption process of the structures by response surface methodology, an optimal sample is selected and simulated; moreover, the identical sample is also subjected to experimental tests. The results showed approximately 272% enhancement in the specific energy absorption of the optimal sample in design of experiments table compared to the weakest one.