Abstract Plastic deformation and fracture in polysynthetically twinned (PST) crystals of TiAl have been simulated by using periodic unit cells representing the relaxed-constraint model recently proposed by Lebensohn et al. [Acta Mater. 46 (1998) 4701–4709] for the co-deformation of the lamellar compound of PST-TiAl. The unit cells contain both intermetallic phases, α 2-(Ti 3Al) and γ-(TiAl). Furthermore, the six orientation variants of the γ-phase are also considered. The constitutive behaviour of both phases is described by crystal plasticity, and the damage behaviour has been implemented by means of cohesive elements. The unit cells have been used as submodels for multi-scale finite element simulations of compression tests and fracture mechanics tests of notched micro-bend specimens. It is shown that the anisotropy of plastic deformation and damage in PST-TiAl can be well represented.