An investigation is made of how the polar electrojet currents and associated electric fields map down to the ground. The boundary value problem which characterizes the downward mapping of the electrojet current will be formulated using potential theory. The electrojet current is represented by a simple Cowling model in which the geomagnetic field is vertical. A numerical solution to the electrojet mapping boundary value problem is obtained via a finite difference technique. This model is employed to study the downward mapping of the polar electrojet current during intense magnetic storms occurring under sunspot maximum daytime conditions. Results of this analysis suggest that as the current maps down through the D region, from an electrojet source in the E region, it is being attenuated as well as rotated. The rotation, however, is not present at altitudes below the D region. A possible application of electrojet mapping theory to the interpretation of high-latitude ionospheric modification data taken during polar electrojet events is discussed. ¿1991 American Geophysical Union