Aiming at a new type of air transport box, this paper studies the influence of the height and angle of convex edge in the coupled concave convex edge structure on the maximum deformation of the box when the box drops. Modal analysis and random vibration analysis of the box are carried out to explore the influence of concave convex edge design in air transportation. Using CATIA to establish the solid three-dimensional model of air transport box design. Referring to the height of the cargo door of various types of aircraft, the finite element software Ansys is used to analyze the falling from the cargo door in the process of handling, and the modal analysis of the transport box is carried out. The maximum deformation and equivalent stress of the random vibration in the process of air transportation are explored. The maximum total deformation and equivalent stress of the box are studied under seven drop conditions, including three kinds of surface drop, three kinds of edge drop and one angle drop. The interpolation surface is established by Matlab software to find the optimal design. In all design schemes, the maximum equivalent stress of the box will not cause material damage. When the height of the convex edge is 20 mm and the angle of the convex edge is 0°, the average maximum total deformation of the box is the minimum. It is determined that the existence of concave convex edge reduces the maximum deformation of the box body, this air transport box will not produce large deformation during air transport, and the maximum deformation is smaller than that of the box without convex edges, which can be put into subsequent manufacturing and use as the optimal design.