The paper deals with the study of the influence of viscosity on the dispersion curves in the case of viscoelastic layer. The material of the layer is described by the Rabotnovs model. Two cases are considered: symmetric stress-strain state (SSS) on the normal coordinate and asymmetric SSS. The properties of modes which change in time harmonically are investigated for the purpose of studying of the free vibrations. Dispersion equations for both cases are derived. The numerical data for different values of the viscoelastic parameters are obtained. They allowed to make conclusions about the influence of viscosity factors on the dispersion curves. Asymptotics for some modes in the vicinity of zero frequency are obtained. It is demonstrated, that asymtotics and the numerical solutions in these vicinities are coinciding.
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