According to the energy principle, the transverse vibration strain energy and kinetic energy of the tied arch bridge are calculated while selecting a sinusoidal wave as the horizontal fundamental frequency vibration mode. Based on the Rayleigh method, the fundamental frequency calculation formula of the tied arch bridge is established. This formula is simpler and more precise compared to the finite element method, and its physical conception is clearer and more definite. The results show that the calculations agree well with the experimental results, and the method and conclusions provide reference for the earthquake resistance design of the tied arch bridge.