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Asymptotic analysis for small long-wave perturbations of a given stationary shear flow of an ideal fluid with free boundary as t → ∞ is performed. It is shown that small disturbances of the flow are attracted to periodic solution in the case where the governing equations are hyperbolic on the main shear flow solution. A class of shear flows for which Landau damping is realizable, is described. Analytical results obtained are validated by numerical calculations.