In this paper, we examine the two-arm conical spiral antenna (CSA) for use in ground-penetrating radars (GPR). Some of the performance characteristics of the CSA in free space such as unidirectional radiation, circular polarization, and frequency independence, would be beneficial in GPR applications when the antenna is operated in a stepped frequency mode. In previous work, it was shown that these characteristics are preserved when the CSA is placed over the ground. The finite-difference time-domain method (FDTD) is used to analyze the CSA over the ground. The model contains all of the details of the antenna, dissipative soil, and buried object. The FDTD analysis is validated by comparing numerical results for the input impedance and the realized gain with measured results that were made wit a pari of identical conical spiral antennas. A parametric study is performed to determined the best antenna geometry for use in a GPR application. The main criterion for this study is to maximize the power transfer into the ground while preserving frequency-independent performance of the CSA over the ground. Antennas with small cone angles are found to be most suitable for this application. The results form this study are used to model a monostatic GPR that uses a single two-arm CSA for transmission and reception. Two different objects buried in the ground are used to illustrate the sensitivity of the CSA to the polarization of the scattered electric field of the target. In the first case, the targets are thin metallic rods that predominantly scatter linear polarization, while in the second case, the targets are buried plastic mines.