The scattering of electromagnetic waves by dielectric cylinders and, in particular, by optical fibres is studied through integral equations. The convergence of the iterations of the integral equations is established under certain conditions. The latter are satisfied for long wavelengths, and for optical fibres and wavelengths, when the dielectric permeability variation is rather small. An approximate eikonal solution is applied to optical fibres, and its reliability is discussed. A systematic procedure for estimating corrections to the eikonal approximation is proposed.