The complex eigenvalue equation of a m etal-clad grade index planar waveguide is solved exactly.The results of the fir st and the second order approximation obtained by using the perturbation theory and multi-layer approximation method are compared with exact results.It is demo nstrated that the perturbation and multi-layer approximati on method gives results in good agreement with those obtained by exact solution of complex eigenvalue equation.It is also demonstrated that the difference betwe en results of the first and the second order approximation is quite small and us ually the first order approximation gives sufficiently accurate results. -