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The contribution is concerned with dynamics of a thin elastic layer, subject to sliding contact. Both one- and two-sided sliding contact are studied, revealing the presence of the fundamental vibration modes. First, mixed boundary conditions modelling two-sided sliding are addressed, allowing a factorisation of the dispersion relation. Then, the asymmetric problem of one-sided sliding contact is tackled, with mixed conditions along the contact surface and prescribed normal stress on the opposite face. Using symmetry, this problem is found to be related to that for a layer of a double thickness, with classical boundary conditions in terms of stresses. In this case, the fundamental mode of interest coincides with the zero-order Rayleigh-Lamb symmetric wave. A long-wave low-frequency perturbation scheme is implemented for the forced problem.