Abstract: The free vibration equation for the horizontal elastic support arch structures is established by the flexibility method. The additional inertia force of the arch foot mass is taken into account. The influence of the horizontal elastic support on the inherent characteristics of the two-hinged arch is analyzed. The natural frequency is shown to be decreased. The influence is the largest at the rise span ratio of 0.1. The horizontal elastic support affects the vibration modes. Especially for higher modes, the horizontal elastic support arch vibrates completely in accordance with the circular beam. The vibration internal force characteristics of the circular beam and the two-hinged circular arch are analyzed. The concept of the flexibility coefficient is put forward. The critical flexibility and the corresponding critical stiffness are obtained.