Polar regions are among the most affected areas by the current global warming. In the Southern Hemisphere (SH), impacts of a warmer climate include decrease in sea-ice extent, changes in oceanic and in atmospheric circulation. Recently, some of these impacts were reinforced by the positive phase of the Southern Annular Mode (SAM). SAM is the dominant mode of variability of the SH extratropical climate and manifests as a "ring-shape" regular pattern of atmospheric mean sea level pressure (MSLP) with opposite sign between mid and high SH latitudes. Over the last three decades, SAM has presented a positive trend, and some studies associate it to stratospheric ozone depletion and to an increase in greenhouse gases concentration. As this debate is still open, climate models constitute useful tools to understand the SH variability in future scenarios. Here we use monthly MSLP outputs from the Brazilian Earth System Model (BESM) to examine SAM temporal and spatial behavior in future climate scenarios compared to the historical period. Our results for the BESM simulations suggest that the mean spatial pattern of SAM does not change with global warming, but an increase in the radiative forcing may reinforce positive SAM values obtained for the historical period.