Position-sensitive CZT detectors for astrophysical research in the five-several hundred keV range are being developed at UCSD and WU. These can be used for large area detector arrays in coded mask imagers and small-area focal plane detectors for focusing X-ray telescopes. The detectors have crossed-strip readout and optimized strip widths and gaps to improve energy resolution. A model of charge drift in the detectors and charge induction on the electrodes has been developed to allow for a better understanding of these types of detectors and to improve their design. The model is described and its predictions are compared with laboratory measurements. In general, there is good agreement between the model and the measurements.