In this study, the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated. The boundary conditions and properties of each beam vary, and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations. By examining a high-speed railway (HSR) with mixed boundary conditions, the rationality for the newly proposed method is verified, the difference in simulated multiple-beam models with different beam numbers is explored, and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined. Results suggest that the number of beams in the model should be as close to the actual beam number as possible. Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure. Neglecting the track-structure can overestimate the resonant speed of a high-speed railway, simply-supported beam bridge. The effective interval of foundation stiffness (EIFS) can provide a reference for future engineering designs.