This paper summarizes the results of the work done by Russian geoscientists in the area of Elbrus volcanic center from the end of the XX to the beginning of the XXI century. It is shown that the results of the geological and geophysical studies of the Elbrus Volcano, including the dating of its historic eruptions, the anomalous velocities of longitudinal waves, the regions of low resistivity, poor tectonic dislocations, the gravity and temperature anomalies, and the resonance specifics of the igneous rocks suggest that Elbrus is an active volcano underlain by molten igneous rocks. The geological characteristics obtained in this study for the geological structures in the Elbrus area can be used for the mathematical modeling of the wave processes induced in the layered rocks of this volcanic cone.