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Annotation. In this paper we consider the spectral problem for the wave propagation in extended plates of variable thickness. Describes how to solve problems and numerical results of wave propagation in infinitely large plates of variable thickness. Viscous properties of the material are taken into account by means of an integral operator Voltaire. The study is part of the spatial theory of viscoelastic. The technique is based on the separation of spatial variables and formulating boundary Eigen values problem to be solved by the method of orthogonal sweep Godunov. Numerical values obtained for the real and imaginary parts of phase velocity as a function of wave number. When this coincidence numerical results obtained with the known data.