In 1915 Galerkin published an article in which he put forward an idea of an approximate method for differential equations, in particular boundary value problems. He had applied his method to a big number of pivot and plate analysis problems. Some time before I.G.Bubnov developed a similar approach for the variational problem solution, which he interpreted as a variant of Ritz method algorithm. The distinguishing features of Galerkin's method were the following: he did not associate the method, developed by him, with any variational problem direct solution, but considered it to be common for solving differential equations. He interpreted it, using the probable displacements principle. These ideas showed to be very productive, not only in structural mechanics, but for mathematical physics at large.