In this paper an efficient way to analyze the scattering from dielectric cylinders is presented. The technique relies on the method of analytical regularization (MAR) (A.I. Nosich, 1999), (M. Lucido et al., 2006), R. Araneo et al., 2002), (M. Lucido et al., 2004) applied to the solution of integral equations. The analytical regularization is achieved by using a Galerkin scheme with basis and testing functions factorizing the correct edge behavior of the electromagnetic field at edges. The outline of the theory and some numerical examples are given.