This work analyzes the propagation characteristics of electromagnetic waves and the frequency selectivity of dielectric gratings with periodicity in two dimensions, having in mind their-application as dichroic surfaces in the millimeter wave band. The moment method and the Green's functions, along with the volume equivalence theorem are used, Particular cases were analyzed to compare with results available in the specialized literature and agreement was observed. This work gives evidence that the inclusion of the periodicity along a second dimension allows an additional adjusting parameter of the frequency selective characteristics for the design requirements of dielectric gratings.213447459