The article is devoted to description base varieties of vault structures arched before XXthcentury. History of studying structural features of vaults and nowadays situation were considered. According to the analysis, the following conclusionsare:

1) at the present time, in spite of technological progress, still has not found the law of stress distribution in the vault body and not a set of criteria developed by the strength and stability; 2) there is no researches which would are deeply engaged in this issuein Russia; 3) the most common way to date the approximate calculation of the vaulted structures is the use of software that take into account the nonlinearity and anisotropy of these structures, such as ANSYS or SOFiSTiK.

Requisite of fundamental research structural behavior have been founded. Vaults of main building St.-Petersburg State polytechnicuniversity were inspected and analyzed.