Crush behavior of different arrangements of multi-tubes filled by functionally graded foams (FGF) are evaluated in this study. Our study shows that the energy absorption of FGF filled multi-tubes is higher than their equivalent multi-tubes filled by uniform foams. Also, the results show that the type of function employed for grading foam has significant effect on their crush response. In this study, multi-objective optimization was carried out using geometrical average and multi-design objective (MDO) methods. The results give new design ideas under axial loading to improve energy absorption performance of FGF foam-filled tubes.