In an experiment described by Fishman et al. [1994>, high energy photons of atmospheric origin were detected by the Burst and Transient Source Experiment (BATSE) detectors, located on the Compton Gamma Ray Observatory (CGRO). In this paper we assess the possibility that the bursts may be bremsstrahlung produced by relativistic (>1 MeV) runaway electron beams accelerated in an avalanche process by quasi-electrostatic thundercloud fields. We consider the height-dependent density profile of the relativistic electrons specified as a function of time in the context of a previously reported runaway model [Bell et al., 1995>. The electron beam is modeled as a vertical cylinder with radius 10 km, and numerical estimates are provided of &ggr;-ray fluxes which would be observed at the satellite. The predicted fluxes at the satellite altitude and at horizontal distances of up to 500 km from the source are found to be comparable to the experimental data. ¿ American Geophysical Union 1996