To evaluate the residual stress in TiAl based alloys by X ray diffraction, X ray elastic constants (REC) of a γ TiAl alloy were determined. From these results, the stress state of a given phase in a duplex TiAl based alloy under a uniaxial tensile loading has been characterized by X ray diffraction. The results show that the X ray elastic constants and the microscopic stresses of the given phase are different from the apparent elastic constants and the macroscopic stresses of the alloy. The reason of the different distribution of the alloy was also discussed. [ To evaluate the residual stress in TiAl based alloys by X-ray diffraction, X ray elastic constants (REC) of a γ TiAl alloy were determined. From these results, the stress state of a given phase in a duplex TiAl based alloy under a uniaxial tensile The results show that the X ray elastic constants and the microscopic stresses of the given phase are different from the apparent elastic constants and the macroscopic stresses of the alloy. The reason of the different distribution of the alloy was also discussed. [