Gravity waves are disturbances whose restoring force is buoyancy. In the atmosphere they are made possible by the variation of potential temperature with height. They can be excited by various mechanisms including flow over orography. The momentum carried by these disturbances can exert significant drag forces on the mean flow in the terrestrial mesosphere. One parameterization of this effect, the Lindzen gravity wave drag scheme, is inserted into two simplified general circulation models (GCMs) of the Martian atmosphere, and its effects are described. The influence of large-amplitude, planetary-scale topography on wave breaking altitudes is discussed. We show that above 60 km in altitude, gravity wave drag dominates the momentum balance of the Martian atmosphere on the largest scales. This indirectly alters the thermal state of the atmosphere through the thermal wind relation. Model winds at this level are consistent with other, simpler studies, as well as with Earth-based spectroscopic observations. Below 60 km, the effects of planetary wave-mean flow interaction, as well as heating associated with Hadley circulation descent, are significant in determining the wind strength. Eddy diffusion coefficients derived from the Lindzen parameterization above 50 km are consistent with values implied from chemical modeling of the Martian middle atmosphere, as well as with simpler models of gravity wave drag.