In this thesis, the full-vectorial finite element imaginary-distance beam propagation method (FE-ID-BPM) based on the hybrid edge/nodal elements and the perfectly matched layers (PMLs) is used to analyze some surface plasmonic waveguides. The metallic rectangular waveguide, the metallic circular waveguide, the metallic holey fiber, and the asymmetric metal stripe waveguide are investigated. The rectangular and circular waveguides in nano-scale perform differently from the perfectly electric conductor (PEC) waveguides popularly used at microwave frequencies. The extended cutoff wavelengths of TE-like modes and TEM-like mode as well as the effects of the wall width, wall height, and wall radius are discussed. The metallic holey fiber is a photonic-crystal-fiber-like (PCF-like) structure with metal injected to a certain air ring, for which the complicated modes include the surface plasmon (SP) modes and the fundamental PCF mode. The effective refractive indices at optical wavelengths of these modes are analyzed. Finally the asymmetric metal stripe waveguide is studied, and especially the leaky modes for which the calculations are refined by using different values of the PML reflection coefficient.