An analytical-numerical technique for the solution of the two-dimensional electromagnetic plane wave scattering by a finite set of dielectric circular cylinders buried in a dielectric half-space is presented. The problem is solved for both the near- and far-field regions, for transverse magnetic and transverse electric polarizations. The scattered field is represented in terms of a superposition of cylindrical waves, and use is made of the plane wave spectrum to take into account the reflection and transmission of such waves by the interface. The validity of the approach is confirmed by comparisons with results available in the literature, with very good agreement, and by self-consistency tests. Applications of the method to objects of arbitrary cross section simulated by suitable configurations of circular cylinders are shown.