The so-called underground Ani is a vast multi-tiered structure of hundreds of cave complexes and separate spaces in the rocks of the Ani Plateau and neighboring gorges. Explored in 1915–1916 by members of the N.Ya. Marr expedition, D.A. Kipshidze and N.M. Tokarskiy, this man-made architectural ensemble hidden in layers of volcanic tuff raised many scholarly questions. Even after the latest research by Italian and Turkish colleagues, they did not drop out. This article examines only one architectural type of these underground monuments: square hypogea with high pyramidal tents. This type of structure, possibly dating back to pre-Christian traditions, is practically unknown outside of Armenia. As a result of our study, we came closer to understanding the architecture of these halls. Despite the existing hypothesis on dating, function, and origin of the halls, we are to propose new solutions, although some more deep studying of these monuments is still needed. Limited historical and archaeological data does not prevent us from discussing the problems of the Ani cave structures in the context of analysis of their architecture. It is necessary to expand the circle of analogies to this type of halls – both in Armenia and in the neighboring regions of the medieval world – to undertake new natural studies of the underground Ani.