Abstract: In order to solve the theoretical calculation problem of the internal force of arch structures with non-ideal boundary constraints, this paper simplifies the non-ideal boundary constraints as elastic support, and simplifies the force method equation based on the elastic center method. The elastic compression is considered and the precise curve integral method is adopted. The analytical solutions are derived for rigid arm length, constant displacement, load displacement and internal force of parabolic arch with elastic support and under vertical moving load. The influences of flexural compression stiffness ratio, rise span ratio and horizontal elastic restraint on horizontal thrust at the support are studied. The influence of horizontal elastic restraint on internal force distribution of arch axis is also studied. The results show that the analytical expression proposed in this paper has a clear physical concept, is correct and reliable, and can explicitly show the influence process of elastic support parameters on internal force calculation. The calculation error of horizontal thrust increases with the increase of bending and flexural compression stiffness, ignoring the influence of elastic compression of arch rib. The calculation error of horizontal thrust is the largest when the arch toe support is a rigid constraint, which can reach 27.8%. Horizontal elastic support can significantly change the distribution of horizontal thrust and arch axis internal force at the support. The influence coefficient of horizontal thrust increases nonlinearly with the increase of rise span ratio. The influence coefficient of horizontal thrust corresponding to the common rise span ratio is about 0.15 when the flexural stiffness ratio is 1.93 and the flexibility coefficient of horizontal elastic support is 0.02.