Accurate modeling of electromagnetic wave propagation in conducting media is important for the further development of ground-penetrating radar technologies. Numerical stability and dispersion criteria are derived here for two common 1--D finite-difference solutions of Maxwell's equations. In one finite-difference scheme one-sided differences are used to approximate the conducting term and in the other centered differences are employed. Stability is governed by the well-known Courant criterion. In addition there is a stability condition controlling the diffusive aspects of wave propagation for the one-sided difference scheme. It is found that the centered difference approximation has significantly better stability and dispersion characteristics. For the centered scheme, the well-known spatial sampling criteria for the non-conducting case are found to be valid for conducting media. The results are tested and illustrated using 1--D synthetic radargrams. ¿ American Geophysical Union 1996