A quasi-static, two-dimensional numerical model of atmospheric electricity that solves the continuity equation of the conduction current has been constructed. This model is used to calculate the local electric structure of the atmosphere in the vicinity of various orographic features and to determine how these features affect the mapping of electric phenomena out of the boundary layer to higher altitudes. The model uses a realistic conductivity profile that includes the equalization layer above 65 km produced by the presence of electrons in the daytime D region of the ionosphere. Anisotropic conductivity resulting from the earth's geomagnetic field is considered in this layer. The results illustrate the dependence of the electric field and current distributions above mountains upon the curvature of the mountain slope, the horizontal scale of the mountain, and the columnar resistance above the mountain (or mountain height). Wide mountains can map current and field distortions upward very efficiently, e.g., a mountain with a height of 3 km and a horizontal scale of 50 km is able to maintain 70% of the increase in the vertical surface current at ionospheric altitudes, while a mountain with the same height and a horizontal scale of 35 km maps only 40%. It is demonstrated that this width effect also exists for a system of mountains. The current above a mountain is always magnified, but the electric field increases above a curved mountain and decreases above a mountain plateau. Horizontal currents also develop around a mountain and can reach values comparable to the fair-weather current. The magnified currents produced by a mountain can extend to ionospheric heights, where the direction of the geomagnetic field lines becomes important and influences the current configuration in the anisotropic region (above about 70 km).