In this Master Thesis two different methodologies for building atomic models of planar faults in gamma-TiAl are implemented. The generalized stacking fault energy for stoichiometric TiAl is calculated within the framework of Density Functional Theory and Molecular Dynamics with the code packages VASP and LAMMPS, respectively. Different energy profiles corresponding to different dislocation dissociation schemes are discussed. The impact on the stacking fault energies for different relaxation methods, varying cell volume and using different exchange correlation potentials is examined. A simple model is implemented to get trends for different alloying elements. The most striking results are that the stacking fault energies depend on the chosen relaxation method due to the fact that their energy minimum do not lie exactly on their hard-sphere model positions and that the ratio (Ti+X)/Al has a huge impact, generally finding lower stacking fault energy values for ratios bigger than 1.