In this work, we are interested in the numerical approximation of an eigenvalu- e problem posed in $\Rd$ arising from the computation of guided modes in integrated optics waveguides, which are particular cases of open waveguides- . We consider a stratified waveguide translationally invariant in the infinite propagation direction. Its cross-section is also supposed to be an unbounded and stratified medium where an appropiate perturbation of the refraction index has been introduced to ensure the existence of guided modes. Under the weak guiding assumption, a method to compute the guided modes has been proposed and analyzed in [11]. This method appears as a combination of analytical methods which take into account the unbounded and stratified character of the propagation medium and numerical computations which can be reduced to a neighborhood of the perturbation. In this paper, we are concerned with the numerical implementation of the method and we present some numerical results.