The horizontal circular loop and the coaxial array of loops above a material half space are studied as antennas for directive transmission into the half space. In a practical situation the loops might be located in air with the directive transmission into the earth. In determining the optimum geometry for the single loop and the array, the far-zone field patterns and directivities of these antennas when placed over lossless dielectrics are considered first. The directive properties for the lossless dielectric are found to be indicative of those for the same antenna over a medium with low loss when proper account is taken of the exponential attenuation experienced in the lossy medium. Parametric studies are used to obtain the maximum directivities for these antennas. For the single loop of resonant size, the optimum height over the interface is determined, and for the two-element array consisting of a driven loop of resonant size with a single parasite, the optimum size and spacing of the parasitic reflector are found. Measured electric field patterns and gains of model antennas above an interface between air and fresh water are in good agreement with the theoretical results.