We have used a two-dimensional numerical model of mesospheric cloud formation to simulate the effects of internal gravity waves on the formation and appearance of ice clouds at the mesopause. We have used gravity wave parameters (amplitude, wavelength, period, etc.) consistent with measurements of gravity waves in the high-latitude mesosphere, including observations of band and billow structures in noctilucent clouds (NLCs). We have investigated both the dynamical effects due to wave-induced winds and the microphysical effects due to wave-induced temperature perturbations. We find that the structures observed in NLC from the ground are predominately caused by dynamical processes. Since the time required for ice crystal growth at the mesopause is much longer than the observed wave periods and ice crystal sublimation is much more rapid than deposition growth, the primary effect of wave-induced temperature perturbations is to decrease the albedo of the clouds. The fact that gravity waves with periods less than a few hours are ubiquitous near the high-latitude, summertime mesopause imposes an additional constraint on the formation of visible NLC. We find that the mean mesopause temperature must be about 5 K colder for NLC to form when gravity waves are present than when they are not present. Long-period (>10 hours) waves may temporarily enhance the brightness of existing NLC but will not induce the formation of NLC.