AbstractMicrostructure of alloys contains typically stochastic distributed constituents (grains) with uneven properties. Recent progresses in computational modelling enable microstructure-sensitive and multi-scale simulations methods, where stochastic properties can be considered with an increasing resolution of local details. In this work a stochastic approach was proposed where several numerical aspects are treated in a finite element framework: (i) determination of grain-wise properties; (ii) the kind of stochastic distribution; (iii) introduction of necessary but appropriate idealizations regarding real microstructure; (iv) use of appropriate constitutive models for deformation, damage and fracture. The proposed stochastic approach was applied and verified on a TiAl polycrystal with significant stochastic nature. The strong anisotropic deformation behaviour, due to the oriented lamellar grains consisting of relevant TiAl phases (α2 and γ), was determined at first by a two-scale crystal plasticity model, and then, the results were transformed to a homogenized grain behaviour corresponding to each oriented lamellar grains. The simulations provide a significant deformation scatter which was used in the presented stochastic approach. Regarding the stochastic evolution of damage till failure, a cohesive model was applied at idealized grains along the fracture plane. Simulation results showed that failure of the first grain was closely related to the macroscopic failure of tensile tests, which provides estimation of grain-wise damage properties. Further, unsymmetrical weighted distribution shapes were introduced to consider inhomogeneous dispersed properties. The cohesive model with these stochastic properties allows a deep and qualified understanding of internal grain-wise damage evolution, first grain failure, and unstable crack extension across the fracture surface. In particular, deformation constraints among grains with different properties play major roles in the evolution of the local damage till component failure.