We present a magnetospheric model of the subauroral polarization stream (SAPS) electric potential, parameterized by Kp index (valid for Kp = 4--7), on the basis of a previous study of the average characteristics of SAPS. The model treats the SAPS westward flow channel as a potential drop whose radial location and width decrease as a function of both increasing magnetic local time (MLT) and increasing Kp. The magnitude of the SAPS potential drop decreases eastward across the nightside and increases with increasing Kp. The model SAPS flow channel significantly alters the flow paths of plasma in the afternoon and evening MLT sectors and agrees with an earlier single-event study that used an ad hoc SAPS potential to obtain good agreement with plasmasphere observations. The model performance is tested via comparison with 13 intervals of plasmapause data obtained during the period 1 April through 31 May 2001 by the extreme ultraviolet (EUV) imager on the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) satellite. Although the model performs well, the current Kp-based parameterization is somewhat crude, capturing only the gross spatial and temporal SAPS characteristics.