The propagation of subsurface radar pulses in complex dielectric media is studied numerically. The model waveform is a 10-ns sinusoidal cycle, and the media properties are similar to those of moist ground or sea ice. When the real part of the dielectric permittivity is frequency independent and the imaginary part is dominated by the dc resistivity, amplitudes of the positive and negative half cycles unbalance, and the sinusoidal zero crossing is delayed from its normal position. In these cases, if reflector depth is known, the dielectric constant can be measured from the time delay of the leading edge of the signal, and the dc resistivity can be estimated from a comparison of the input and output pulse power spectra. When dielectric permittivity is frequency dependent through a simple relaxation process, waveform distortion depends on relaxation frequency. In addition, if reflector depth is known, the dielectric relaxation parameters εs and ε∞ may be estimated when the medium relaxation frequency lies above and below the major portion of the pulse bandwidth, respectively.