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In many materials with low crystal symmetry or low stacking fault energies plastic deformation occurs not only by crystallographic slip, but also by twinning. Several proposals have been made to implement mechanical twinning into texture modeling, for example the predominant twin reorientation (PTR) scheme of Tomé. The grain interaction (GIA) model is one of the most advanced cluster type Taylor models, and has been successfully applied to predict the deformation texture evolution of cubic materials, especially Al and its alloys. In this study we use the PTR approach to handle twinning in the GIA model, and applied a modified GIA model to simulate deformation texture evolution of Mg alloy AZ31 at different temperatures. Two different values of critical shear stress were employed for twin nucleation and growth. The simulation results, such as the final textures at several temperatures and the texture evolution for certain strain intervals, were compared with experimental data. An overall good agreement between simulation and experiment were observed, but the PTR scheme predicted the twinning process to proceed faster than observed experimentally. The texture predictions were improved by setting two critical resolved shear stress values for twinning.