The theory of scattering of higher-order Gaussian beams by an infinite
cylinder with arbitrary location and arbitrary orientation is present
ed. An ingredient of the theory is the use of distributions. Gaussian
beams are described by using the so-called standard description, the l
ocalized approximation and the modified localized approximation in a u
nified framework. Computations are explicitly carried out up to terms
which are O(s(10)), in which s is the beam confinement parameter.