Propagation characteristics of the Er-doped waveguide amplifier are studied by the variational method. The variational expression of the propagation constant is proposed in the buried ion-exchanged glass optical waveguide. The unknown parameters of the Hermite-Gaussian trial solution for the field profile are determined by using the variational method. The field distributions of different fabricated waveguides are then determined. The propagation constant and the effective refractive index are calculated using the variational expression of the propagation constant and the determined field distributions. The fact that the effective refractive index is slightly larger than the bulk index shows that the waveguides fabricated are weak ones. High electrical intensity and short annealing time are shown to be useful in the fabrication of buried waveguides. The calculation procedure is simple and the results calculated using the variational method agree with those measured in the experiment.