Intense, transient quasi-electrostatic (QE) fields, which exist above thunderclouds following a positive cloud-to-ground lightning discharge, can produce an upward travelling runaway electron (REL) beam. A new two-dimensional (2D) REL-QE model is developed, expanding the previously reported 1D model [Bell et al., 1995> and incorporating the QE [Pasko et al., 1997a> and the recently developed electrostatic heating (ESH) [Pasko et al., 1997b> models. The new model gives the lateral electron distribution in the beam and allows us to determine the ionospheric effects and the optical luminosities resulting from the simultaneous action of the QE fields on the ambient electrons and the runaway electrons. The model is self-consistent and includes the changes in space charge and conductivity due to the REL. Optical emissions and &ggr;-ray emissions [Lehtinen et al., 1996a> are calculated and compared to experimental observations of Sprites and terrestrial &ggr;-ray flashes (TGF). It is shown that the structure of the electric field and the optical emissions can be significantly affected by the REL.¿ 1997 American Geophysical Union