Polycrystalline Titanium-Aluminides (TiAl) are very interesting materials for the aerospace industry. Their low density, combined with a high Young's modulus, render them prime candidates for industrial applications at temperatures up to 800°C. However, the principal obstacle to widespread utilisation remains their low ductility (around 2%) at room temperature. This limited ductility is the consequence of an early damaging of the microstructure, due to the low number of straining mechanisms involved during the deformation process. This gives rise to strain heterogeneity in the polycrystal, thereby causing incompatibilities and microcracks. The aim of this study is to predict, for macroscopic tests carried out at room temperature, the occurrence and the localization of microcracks directly from the actual microstructure and the straining mechanisms involved. In order to identify the parameters of the crystallographic constitutive law, the experimental strain field, obtained by an imaging correlation technique, has been coupled to finite element simulations carried out at the same scale. The difference between the experimental and calculated strain fields is then minimized using a genetic algorithm.