In this work, an accurate and efficient iterative numerical approach suitable for the analysis of 3-D guided wave structures is presented. The proposed method is fully vectorial and based on the transverse magnetic field formulation. In order to enhance the computational efficiency of the proposed method, a hybrid implementation is utilized using Pade approximants in tandem with a reduced spectrum of eigenpairs. The present formulation can account for the presence of strong and multiple longitudinal discontinuities. Convergence of this iterative approach is achieved by the use of a simple preconditioner. The accuracy and efficiency of the proposed method are demonstrated by applying it to two different guided wave structures with multiple longitudinal discontinuities.