The integral equation method have been used to set up the physical model of the wave transmission in the beam waveguide. The Mode Matching method has been used to describe the matching situation at the exciting aperture. The Multilevel Fast Multipole Algorithm (MLFMA) has been used to accelerate the calculation. The Phase Extraction (PE) basis function is used to discrete the electric current. It has been demonstrated that the method proposed by this paper is able to provide the accurate solution for the excitation, propagation and radiation problems of the beam waveguide with arbitrary shape and electrically large size efficiently. Index Terms -Beam waveguide, integral equations, Multilevel Fast Multipole Algorithm, PE basis function.