Quasi-brittle fracture of fully lamellar two phase (α2+γ)TiAl is investigated both experimentally and numerically. Fracture tests are conducted at room temperature, which fail in a quasi-brittle and unstable manner but exhibit significant variations in crack initiation and propagation prior to unstable failure. Fractographic investigations are performed which elucidate the micromechanical causes of the macroscopic behaviour. The observed deformation and fracture behaviours of the specimens are simulated by a finite element model containing cohesive elements for modelling the material separation. In order to capture the scatter of the macroscopic behaviour, a stochastic approach is chosen, in which local variations of cohesive parameters are taken into account. The model can describe and explain the physical phenomena of the specific material.