Reservoirs and tailings ponds for the mining industry relate to hydraulic structures, presenting a potentially high risk, since their damage may be accompanied by serious socio-economic and environmental consequences. The design, construction, and operation of such facilities in seismically active areas require special approaches and safety measures. The main goal of the article is to identify general issues related to the seismic vulnerability of dams and other enclosing structures in Armenia in order to attract the attention of specialists and decision-makers to this problem. By considering important issues in light of modern requirements and views, some new data have been obtained on the seismic hazard and risk of reservoir dams and tailings ponds. It is concluded that the seismic risk of the territories of most reservoirs and tailings ponds in the Republic of Armenia is high due to the vulnerability of dams and enclosing structures. And its seismic resistance does not meet modern regulatory requirements for various reasons. General recommendations are offered for conducting the necessary new research, in particular, seismic, engineering-geological, etc. in order to increase the safety of the structures in question.