Abstract <p>Foam aluminum, as a new type of filling composite structure, has good energy absorption characteristics. In this paper, the quasi-static compression experiments of thin-walled square tube filled with foam aluminum and foam aluminum are carried out respectively, and analyze its deformation process and stress-strain changes. According to the shape and size of holes randomly and irregularly arranged in porous foam aluminum, the two-dimensional random distribution model of gradient foam aluminum material was established by Digimat and filled into a square tube. Ansys is used to simulate the quasi-static compression and impact of thin-walled square tube filled with gradient foam aluminum. The validity and validity of the two-dimensional random distribution model are proved by comparing the experimental and simulation results. The results show that under the same impact displacement, the energy absorption effect of gradient foam aluminum square tube is better than that of homogeneous foam aluminum square tube of the same mass. In order to further improve the impact resistance of foam aluminum square tube, so that its pressure can be evenly distributed and transferred to other parts of the tube, the energy absorption and peak stress are taken as optimization objectives, and a multi-objective optimization model of gradient foam aluminum filling structure is established. The Latin hypercube design method is used to select design variables, and the selected design points are brought into the model for simulation to build the response surface, and the optimal size parameters of foam aluminum filled square tube under impact conditions are obtained. It provides a reference for the design and application of gradient foam aluminum square tube in compression.</p>