The finite-element method has been used for analyzing open microstrip line structures on highly lossy substrates. The geometry descritization has been carried out by using quadrilateral elements, and the spurious solutions art avoided by employing tangential vector formulation. The difficulties associated with finding the propagation constant of a highly lossy structure 13.1, solving a generalized eigenvalue problem are discussed. A methodology is presented,for a fast and efficient computation of the attenuation and propagation constants of the lossy transmission lines. Numerical results are presented to illustrate the application of the proposed approach for the case of an open microstrip line. (C) 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 325-329, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10908.