When a gamma-ray telescope is placed in Earth orbit, it is bombarded by a flux of cosmic protons much greater than the flux of interesting gammas. These protons can interact in the telescope's thermal shielding to produce detectable gamma rays, most of which are vetoed. Since the proton flux is so high, the unvetoed gamma rays constitute a significant background relative to some weak sources. This background increases the observing time required to pinpoint some sources and entirely obscures other sources. Although recent telescopes have been designed to minimize this background, its strength and spectral characteristics were not previously calculated in detail. Monte Carlo calculations are presented which characterize the strength, spectrum and other features of the cosmic proton background using FLUKA, a hadronic cascade program. Several gamma-ray telescopes, including SAS-2, EGRET and the Gamma Ray Imaging Telescope System (GRITS), are analyzed, and their proton-induced backgrounds are characterized. In all cases, the backgrounds are either shown to be low relative to interesting signals or suggestions are made which would reduce the background sufficiently to leave the telescope unimpaired. In addition, several limiting cases are examined for comparison to previous estimates and calibration measurements. Yearian, Mason R. Unspecified Center...