Abstract: An exact solution for the vibration of arches subject to forces of denotation is obtained by employing a modal superposition method. As to the complicities of the problems of an arch, some simplifications are made, such as the effect of shear, rotary inertia and tangential forces are neglected and the arch is supposed to be incompressible. In order to simulate the forces applied on the underground structure, the soil-structure interaction is considered using a damping coefficient. An arch element with an opening angle of 120°is used for calculating and the responses of displacements, velocities and accelerations are obtained. The relation between the maximum response and the scaled distance is analyzed and the figure is plotted. According to the suggested method, maximum internal forces of each cross section of the arch can be calculated.