In order to study the scattering characteristics of the incident beam by an infinite cylinder with arbitrary regular cross section, the semi-analytical method was proposed. Appropriate cylindrical vector wave function was used to expand the scattered field and internal field, and the expansion coefficient was determined by electromagnetic field boundary conditions and projection method. The normalized near-field intensity distribution was numerically simulated by the example of an infinite cylinder with circular, elliptical and rectangular cross-sections irradiated by a fundamental mode Gaussian beam and a radial annular beam. The results show that, there is obvious interference phenomenon after the beam propagates through the cylinder and elliptic cylinder, and the rectangular cylinder has a certain convergence effect on the beam. This study provides a convenient semi-analytical solution for solving the scattering of arbitrary beams by an infinite cylinder with arbitrary regular cross section.