The capability of frequency-swept cross-borehole radar to detect an empty rectangular cylinder embedded in a dielectric medium is simulated numerically by employing the boundary element method. The frequency loci providing the strongest double dips in the received signal pattern are plotted as functions of the observation distance and the cross-sectional width. It is found that, regardless of the shape of the rectangular cross-section, the strongest double dips become double nulls in the near-field region.