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The aim of the present article is to investigate the surface waves in anisotropic, elastic solid medium under the influence of gravity. The theory of generalised surface waves has first been developed and then used to investigate particular cases of waves, viz., Stoneley, Rayleigh, and Love. The wave velocity equations have been obtained for different cases and are in well agreement with the corresponding classical result, when the effect of gravity, viscosity, and fibre-reinforced parameters of the material medium are ignored.