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We employ the eigenmode analysis approach based on finite element method to calculate the dispersion relation of the surface plasmon modes in metallic nanostructures. Firstly,  benchmark results are demonstrated in metal/dielectric interface, metallic film and single nanowire. Then we focus on the metallic bi-nanowire system which has been proposed as a robust surface plasmon waveguide. We calculated the field patters, charge distributions and dispersion relations of all the surface plasmon modes existed in such system and found some interesting coupling effects. This approach can be also applied to two-dimensional (2D) or three dimensional (3D), dispersive, anisotropic, and complex shaped systems.