In this paper we construct conjugate spectral problem and the conditions of biorthogonality for distribution in extended plates of variable thickness of the problem considered. It describes the procedure of solving problems and a numerical result is on wave propagation in an infinitely large plate of variable thickness. Viscous properties of the material are taken into account by means of an integral operator Voltaire. Research is conducted in the framework of the spatial theory of visco elastic. The technique is based on the separation of spatial variables and formulates the boundary eigenvalue problem that can be solved by the method of orthogonal pivotal condensation Godunov. Numerical values obtained the real and imaginary parts of the phase velocity depending on the wave numbers. The numerical result coincides with the known data.