Abstract: The contact stiffness at the interface between the columns and connecting beams directly affects the dynamic characteristics of the gantry structure in wire laying equipment. Taking into account the three-dimensional microstructure of the interface and the discrete nature of contact asperities, a critical equation for unit cell deformation was established based on Hertzian contact and fractal theory. By introducing a domain scaling factor, three-dimensional fractal models for contact area, normal load, and contact stiffness were established, elucidating the mechanisms by which fractal dimension and surface roughness parameters affect normal contact stiffness. A box-type specimen was designed based on the shape of the gantry structure’s interface, and a simulation method for analyzing the dynamic characteristics of the gantry structure—taking into account the normal contact stiffness of the interface—was proposed. Compared with the results of impact tests, the maximum relative error between the two was 3.27%. On this basis, dynamic characteristic tests were conducted for gantry structures, and it was found that the relative error between the simulation results and experimental data considering contact stiffness of the gantry structure was 0.18%–5.16%, verifying the effectiveness and accuracy of the analysis method.