Electromagnetic tunnel detection is studied numerically using a 3D analytic infinite lossy homogeneous space solution to magnetic dipole radiation and scattering from an infinite cylinder, in a crosshole context. At low frequencies, this serves as a model for a transmit coil radiating a time-varying magnetic field that is then detected from the open-circuit voltage induced on a receive coil. Numerical simulations illustrate how various parameters influence the signal strength and the ability to discern the scattered signal. Tunnel detection is achieved at relatively high frequencies (but below typical ground-penetrating radar frequencies) for fresh water-saturated sand and for weathered granite, which are lower loss media; for the coil and tunnel parameters used here, the optimum frequencies appear to be between 100 kHz and 1 MHz. Tunnel detection for fresh water-saturated clay, a much more lossy medium, can be achieved at a quite low frequency, with an optimum frequency between 1 and 10 kHz. These results suggest that, when a resonant coil system is used, tunnel detection may be possible in a wider range of earth media than previously reported, when the best-suited choice of frequency is used.