The wave field near defect, edge or load represents a superposition of propagating and non-propagating modes. It is necessary to investigate the non-propagating wave characteristics if the wave scatter and edge resonance should be taken into consideration. In this paper, a modified orthogonal polynomial approach was developed to computationally solve, for non-dissipative materials, the propagating waves given by pure real roots and non-propagating waves given by pure imaginary and complex roots. The dispersion curves giving real part wavenumber and imaginary part wavenumber as functions of the angular frequency are obtained. The results for an isotropic plate and a cubic plate are calculated to make the comparison with exact results. The dispersion curves for a plate with a rectangular cross section are also illustrated. The displacement amplitude variations are illustrated in the vicinity of the frequency where the non-propagating wave becomes a propagating one