An analytical-numerical technique for the solution of the plane-wave scattering problem by a set of dielectric cylinders embedded in a dielectric slab is presented. Scattered fields are expressed by means of expansions into cylindrical functions, and the concept of plane-wave spectrum of a cylindrical function is employed to define reflection and transmission through the planar interfaces. Multiple reflection phenomena due to the presence of a layered geometry are taken into account. Solutions can be obtained for both TM and TE polarizations and for near- and far-field regions. The numerical approach is described and the method is validated by comparison with examples given in the literature, with very good agreement. Results are presented for the scattering by a finite grid of three cylinders embedded in a slab.