The paper deals with the spread of its own waves on the visco elastic plate with variable thickness. Basic relations of the classical theory of plates of variable thickness obtained on the basis of the principles of virtual displacements. The spectral problem, which is not self ad joint. Built for the task biorthogonality conditions, based on the Lagrange formula. The numerical solution of the spectral tasks performed on the computer software system based on the method of orthogonal shooting S.K. Godunov in combination with the method of Muller.