AbstractAn advanced model incorporating a two-scale structural description with integrated constitutive formulations of crystal plasticity was adopted to describe the mechanical behaviour of a γTiAl polycrystal with grains of staggered (γ/α2)-phase lamellae. The numerical model assembles a polycrystalline compound of 64 lamellar grains generated from periodic unit cells (PUC) taking relevant phase configurations. The representative parameter set for the crystal plasticity are estimated by modelling the lamellar deformation and fitting the compression and tension test results in two steps: firstly, the fundamental parameters were identified for a poly-synthetically twinned single crystal (PST) under compression, and secondly, these PST parameters were adjusted to the γTiAl polycrystal consisting of fully lamellar grains. Numerical results show that the compression–tension anomaly in the stress–strain curves can be successfully described by a ‘high-grade’ PUC model including six domain variants of the γ-phase occurring in the lamellae. Using a PUC model with simplified mapping of lamellar microstructure, the prediction quality remains unsatisfactory with respect to the observed compression and tension anomaly and the crystal parameters are found to be inconsistent. Differently aligned lamellar grains in polycrystalline cubic model are predicted, which showed that the global stress–strain curves are weakly affected by different local alignments (or textures) of the grains, whereas, the single grain analyses show strong variations in local stress–strain curves. The simulated nature of local variations in grain scale stress–strain behaviour accords with the independent results from instrumented indentation testing of the same lamellar polycrystal.