An efficient model for Erbium-doped optical amplifiers is presented in this paper. This model, based on an iterative finite-element stationary (modal analysis) scheme in conjunction with a suitable multi-level rate equations system, permits a direct computation of the complex propagation constant β. In addition, the use of absorption/emission cross section parameters permits the computation of the gain, related to Im{β}, and induced nonlinearities, related to Re{β}, over a wide band spectrum (1.40 - 1.65μm). Since up-conversion and cross-relaxation effects are taken into account, the model is also able to analyze highly doped waveguides. Comparisons with other approach and experimental data validate this model.