Abstract-In this paper, a new analytically regularizing method, based on Helmholtz decomposition and Galerkin method, for the analysis of the electromagnetic scattering by a hollow finite-length perfectly electrically conducting (PEC) circular cylinder is presented. After expanding the involved functions in cylindrical harmonics, the problem is formulated as an electric field integral equation (EFIE) in a suitable vector transform (VT) domain such that the VT of the surface curl-free and divergence-free contributions of the surface current density, adopted as new unknowns, are scalar functions. A fast convergent secondkind Fredholm infinite matrix-operator equation is obtained by means of Galerkin method with suitable expansion functions reconstructing the expected physical behaviour of the unknowns. Moreover, the elements of the scattering matrix are efficiently evaluated by means of analytical asymptotic acceleration technique.