Our calculations indicate that regions above large mesocale convective systems may be favorable electrical environments for the production of gamma radiation by runaway electrons in bremsstrahlung collisions. It is well known [Gurevich, 1961> that an electric field however small can accelerate an electron continuously until the electron leaves the region of the electric field, as long as the electric field is larger than the opposing force of friction. Since the force of friction is proportional to the density of air, the reistance on an electron decreases with altitude. The resistance can be expressed in terms of a critical field, which is the strength the field needs to exceed in order to initiate the runaway phenomena. The critical field characterizing the friction is between 7¿10-15 and 15¿10-15 V-cm2 times the number density of air. Thus a resonable electric field (500 V/m) at high altitudes results in a force that can be larger than the force of friction. The rate for producing high energy electrons by the electric fields over large thunderstorms is estimated from Gurevich's model of runaway electrons in a weakly ionized plasma. It is found that the number of gamma photons produced by the runaway electrons in the discharge volume is consistent with the data recently observed by satellite [Fishman et al., 1994>. ¿American Geophysical Union 1995