The stone vaults of historical buildings are considered, which, due to a decrease in bearing capacity, require repair and restoration work. An analysis is given of the mechanisms of destruction of cylindrical vaults depending on the ratio of their height to the span. The advantages of strengthening the vaults with the help of reinforcement with composite materials are analyzed. A description is given of the technology of surface reinforcement of stone structures using composite materials on a polymer cement matrix FRCM (Fiber Reinforced Cementitious Matrix). The technique of experimental studies of models of reinforced and non-reinforced vaults is given. On the basis of the experiment, it is shown that the effectiveness of the reinforcement of the vaults is determined by the features of their stress-strain state and failure mechanisms. In particular, the effectiveness of reinforcement increases with an increase in the ratio of the height of the vaults to its span. These results are substantiated by the fact that in high arches the ratio of bending moments and longitudinal forces is dominant, and in the case of flat arches, longitudinal and transverse forces dominate in their sections, and destruction occurs in the form of shearing along inclined sections. Also, the effectiveness of reinforcement increases with their asymmetric loading relative to the middle of the span. According to the results of the study, graphs of the dependence of the maximum vertical displacements of the vaults were constructed, showing a significant effect of reinforcement on increasing their rigidity. In addition, it is emphasized that by now there is a need for a stable theory of the strength of complex stone structures - curvilinear, vaulted and others that are in a complex stress state. Its appearance can significantly simplify and unify the calculations made when examining stone buildings, drawing up projects for their restoration and reconstruction, and solve the problems of the strength of the masonry of modern facade systems.