Air core waveguides with very low losses can be designed by removing a line of rods at the center of a periodical arrangement of elliptical metallic rods in a square lattice. The use of composite nanostructures made possible the engineering of the cladding properties of the waveguides to present very low equivalent refractive index. The mechanism of propagation in these kind of guides is the total external reflection. In this work, the dependence of the transmission properties of these waveguides on the shape and orientation of the metallic elliptical wires are analyzed by an efficient frequency domain finite element approach. © 2006 SBrT.