The mapping of thundercloud electric fields at middle and subauroral latitudes is investigated analytically as a three-dimensional boundary value problem. The electrical conductivity is represented by several piecewise exponential functions of altitude, and the anisotropy of the medium is taken into account above 70-km altitude. The geomagnetic field lines are assumed to be straight and vertical below 150-km altitude. Electric field strength at great heights depends sensitively on conductivity and thundercloud models used in the calculations. Sample calculations using representative nighttime profiles show that ‘giant’ thunderclouds can produce transverse electric fields of tens of microvolts per meter in the equatorial plane of the midlatitude magnetosphere. In the daytime, corresponding electric fields are about an order of magnitude less. These results suggest that giant thunderclouds may be an important source of localized electric fields that can form field-aligned electron density irregularities in the ionosphere and the magnetosphere.