The detection of methane at Gale crater by the Tunable Laser Spectrometer-Sample Analysis at Mars instrument aboard the Curiosity rover has garnered significant attention because of the implications for the presence of Martian organisms (Webster et al., 2015, https://doi.org/10.1126/science.1261713). Methane's photochemical lifetime is several centuries unless there is a fast, as-yet-unknown destruction mechanism (Lefevre and Forget, 2009, https://doi.org/10.1038/nature08228). This is much longer than the atmospheric mixing time scale, and thus, the gas should be well-mixed except when near a source or shortly after a release. Although most measurements report low background levels of similar to 0.4 parts per billion by volume, observed spikes of several parts per billion by volume or greater and a subsequent return to the background level are intriguing (Webster et al., 2015, https://doi.org/10.1126/science.1261713). The Mars Regional Atmospheric Modeling System is used to simulate, via passive tracers, the transport and mixing of methane released inside and outside of the crater from instantaneous and steady state releases, and to test whether the results are consistent with in situ observations made by the Mars Curiosity rover. The simulations indicate that the mixing time scale for air within the crater is approximately 1 sol. The timing of methane measurements within the crater is also important, because modeled methane abundance varies by similar to 1 order of magnitude over a diurnal cycle under all the scenarios considered. While the observed low background levels can be reproduced by the model under some circumstances, it is difficult to reconcile the measured peaks with the modeled transport and mixing. For periods of high methane abundance lasting longer than a few hours there must be a continuous release of methane inside the crater to counteract mixing, or there must be a large, methane-rich air mass continually transported into the crater. The few scenarios that can produce peaks are problematic, because they would result in background methane values above what is observed.