Large quasielectrostatic (QE) fields above thunderclouds [Pasko et al., 1995> produce an upward traveling beam of ~1 MeV runaway electrons which may contribute to the production of optical emissions above thunderclouds referred to as Red Sprites. Results of a one dimensional computer simulation model suggest that the runaway electrons can produce optical emissions similar in intensity and spectra to those observed in Red Sprites, but only for large QE fields produced by positive CG discharges lowering 250 C or more to ground from an altitude of at least 10 km. Differences in predicted optical spectra from that of other mechanisms suggest that the runaway electron mechanism can be readily tested by high resolution spectral measurements of Red Sprites. ¿ American Geophysical Union 1995