The object of the presented studies is a concrete spillway dam of a run-of-river hydroelectric power station. The modes of vibrations are determined on the basis of a solid model, which is necessary to take into account possible resonant phenomena in the structure. A review of publications on the method of calculating the dynamic responses of structures is made. Computational studies were carried out by the finite element method based on the calculated three-component accelerogram. When processing the results, the possibilities of modal temporal calculation were used. The response of structures excited by forces, time-varying or earthquake is calculated. Based on the calculation results, the natural frequencies and vibration modes of the concrete spillway dam were determined. The description of the oscillations of the dam is made. According to the obtained response spectrum, the maximum horizontal accelerations were achieved. Based on the response spectra, a calculated three-component accelerogram was synthesized at the equipment installation marks.