A sloshing problem in a surge (horizontally) excited partly filled reservoir is considered. Obtaining of free surface elevation by the variational method in two-dimensional problem leads to the system of a non-linear differential equations. This system is analytically solved when the frequency of exciting is equal to the first natural frequency of fluid inside the reservoir. The asymptotic method of Krylov and Bogolubov is used. The expression of free surface elevation is given for the two-dimensional rectangular reservoir.