This paper presents an efficient solution for solving the generalized eigenvalue equation arising in the finite-element (FE) formulation of propagation characterization of planar transmission-line structures. A two-dimensional (2-D) finite-element method (FEM) is used for analyzing the uniform planar transmission lines. The Arnoldi algorithm is used in conjunction with the multifrontal decomposition of the system matrix for solving the eigensystem. Convergence is typically obtained within a few iterations of the Arnoldi process, and the formulation has proven to be robust, even when dealing with a significantly large number of unknowns. Numerical results are presented for the case of a uniform microstrip line, which clearly show the computational savings resulting from the use of the present approach. (C) 2001 John Wiley & Sons, Inc.