Surface Plasmon polaritons are surface electromagnetic waves that are bound to the interface between two media having opposite sign in the real part of their permittivity. The most important feature of surface Plasmon polariton is the exponential decay of the field components on either side of the interface in transvers direction. Metals exhibit negative dielectric constant at visible and infrared wavelengths. As such, the metal-dielectric interface has become a topic of interest in guiding surface Plasmon polaritons. In a plasmonic waveguide, the light can be guided along the metal surface with sub wavelength lateral dimentions enabling the possibility of high density integration of optical elements. Metallic film of rectangular cross section embedded in a dielectric is used as a waveguide in the optical integrated circuits. It can support the long range surface Plasmon polariton modes. Tight field intensity confinement to the metal surface (typically on the order of or smaller than the wavelength in the corresponding media) makes surface Plasmon polaritons very sensitive to surface roughness. One may consider rough surfaces, with a profile that has random character, or with periodic grating of some profile has been impressed on the surface. Here we consider rough surfaces as periodic grating with sinusoidal profile or symmetric sawtooth profile. Two methods of calculation studied are the reduced Rayleigh equation method and the extinction theorem integral equation method. In this thesis we obtain the dispertion relation for surface Plasmon polaritons propagating across a grating, when the sagittal plane is not perpendicular to the generator of the surface. Then we obtain the dispertion relation for a surface Plasmon polariton propagating across a metal slab and rectangular waveguide upon which a periodic grating has been impressed in one face. Propagation properties of surface Plasmon polariton modes in rectangular waveguides are analyzed by the effective index method which uses a simplified model of two perpendicular slab waveguide. New method based on effective index consideration is proposed to determine the propagation characteristic of rectangular dielectric waveguides. Keywords: Surface plasmon polaritons, roughness, reduced Rayleigh equation method, extinction theorem integral equation method