Numerical modeling of thin-wire antennas is interesting to people working on antenna design and to people working on the processing and interpretation of radar data. They have different demands regarding the output of the model code. Our primary interest lies with improving image resolution through processing of ground-penetrating radar data. For this goal the effects of two antennas placed close together on the Earth's surface are studied. To study the antenna to antenna coupling and antenna to ground coupling, a model for linear dipoles is used. The model uses a thin-wire approximation for the transmit and receive antennas. The antennas are placed just above the air-Earth interface. The Earth is modeled as a horizontal layer stack. Using this model, we study the coupling effects between two parallel antennas, either in each other's E-plane or H-plane. For ordinary antenna distances, the coupling between two parallel antennas when they are resistively loaded is on the order of -70 dB, which is not negligible for GPR applications. The influence of the lower half-space on antenna behavior is strong but limited to a fraction of the wavelength in depth.