TiAl alloys can be used in aircraft and high-performance vehicle engines owing to their structural stability at high temperatures and their light weight. Although many studies have focused on developing this alloy material, there is still a lack of information about the changes in the structure of TiAl alloys under tensile and compressive loading. Therefore, we performed molecular dynamics simulations of the tensile and compressive loading of TiAl alloys in the <001> direction at temperatures of 10 and 300 K. From our simulation results, we found that the tensile and compressive strengths of TiAl alloys are significantly affected by temperature. It was found that TiAl alloys can withstand greater compression loading than tensile loading. This is due to the change in the crystal structure of TiAl alloys after being deformed to a strain of 0.4 by compressive loading, according to the analysis of structural changes under loading conditions. From the radial distribution analysis results, there was a change in the orientation of the face-centered cubic-like structure as it reached the maximum compressive stress compared to the initial structure.