To make up for the limitations of high-dimensional engineering structure finite element analysis in structural parameter optimization design, this paper studies the in-plane free vibration of Long-span Arch Bridges Based on Euler Bernoulli beam theory and transfer matrix method. Firstly, based on the stiffness analysis of multi span arch bridge, the global dynamic model of the system is established. Secondly, the global dynamic theory of the system is established based on the transfer matrix method. Finally, the natural frequency and vibration mode of a four span through arch bridge are solved by using the plane mechanical model, and the results are compared with the finite element analysis results modeled with the same parameters, which proves the effectiveness and accuracy of the theory established in this paper for solving this kind of problems. In addition, by changing the rise span ratio of each span of the whole bridge, the sectional area of suspenders and the moment of inertia of arch ribs, the variation trend of the natural vibration frequency in the plane of the system is analyzed. The results show that with the increase of the rise height of the arch bridge, the natural frequency of the system decreases, and the rapid increase of the quality of the arch bridge has a significant impact on the stiffness of the whole bridge deck; Increasing the cross-sectional area of the suspender can increase the in-plane stiffness of the arch bridge to a certain extent, resulting in the increase of the system frequency within a certain range, and the veering phenomenon is observed.