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The deformability and strength of lamellar two-phase (γ and α₂) TiAl alloys strongly depends on the mechanical properties of the different interfaces in such microstructures. We carried out ab-initio density functional theory calculations of interface energy and strength for all known interface variants as well as the corresponding single crystal slip/cleavage planes to obtain a comprehensive database of key mechanical quantities. This data collection can be used for meso-scale simulations of deformation and fracture in TiAl. In spite of the different atomic configurations of the lamellar interfaces and the single crystal planes, the calculated values for the tensile strength are in the same range and can be considered as equal in a meso-scale model. Analysis of generalized stacking fault energy surfaces showed that the shear strength is directional dependent, however, the [112] direction is an invariant easy gliding direction in all investigated systems. The probability of different dislocation dissociation reactions as part of a shear deformation mechanism are discussed as well.