A finite-element analysis, with the aid of perturbation techniques, is used to determine the complex propagation characteristics of surface-plasmon modes that are supported by metal-dielectric interfaces. Symmetrical and nonsymmetrical three-layer optical waveguides incorporating a thin metal layer are studied, and the variations of the effective index and the attenuation constant with metal thicknesses are presented for both the short-range and long-range modes. Results are compared with previously published research, which was based on alternative approaches. Furthermore, for the first time to our knowledge, the complex propagation characteristics are presented for a coupled structure incorporating a surface-plasmon region with two-dimensional confinement.