The beam on elastic supports is often considered as a beam on a continuous elastic medium. This method can be applied only to a large number of equally spaced supports having equal rigidities. The method proposed by the author, giving the solution in the form of rapidly converging series, is not bound by this restriction, and when applied to the problem of beams supported by cross-girders reduces it to a system of linear equations, their number being equal to the number of cross-girders, while the existing approximate method leads to the same number of simultaneous differential equations.