Planning Systems Incorporated (PSI) has developed a promising Ground Penetrating Synthetic Aperture Radar (GPSAR) system to detect buried landmines. GPSAR can be used to generate three-dimensional (3-D) mine images. It has been shown that the SAR processing in the PSI GPSAR system can greatly improve the image quality and hence the mine (especially plastic mine) detection performance. In this paper, two special issues on SAR processing for the PSI system are addressed. One issue is the analysis of the effect of the underground electromagnetic (EM) wave propagation velocity uncertainty on SAR processing and the other is channel mismatch on SAR processing. Since the EM wave propagation velocity in the soil depends on many factors and changes from one location to another, velocity uncertainty is inevitable. However, we have found that the PSI GPSAR system is very robust against the velocity uncertainty. More specifically, velocity uncertainty does not defocus the image but only scales the image along the depth dimension, and hence will not affect the mine detection performance. Another issue is how to select a good SAR processing scheme for the PSI system. Because the radar footprint is 2-D (along-track and cross-track dimensions), 2-D SAR processing may be used. However, the effectiveness of the 2-D SAR processing depends on the coherence of the radar antenna system. Moreover, the computational expense of the 2-D SAR processing is much higher than that of the 1-D SAR processing (along-track dimension only). We have found that due to the channel mismatch of the PSI system, the 2-D SAR processing does not greatly improve the quality of the SAR images when compared with 1-D SAR processing. Hence, without proper antenna calibration, the computationally more efficient 1-D SAR processing may be preferred for the PSI system.