  We investigate the influence of crystallographic twins on the elastoplastic
response of $\gamma$-TiAl intermetallics via full-field FFT-based computations.
We first introduce a hierarchical stochastic model, which is used to simulate
synthetic polycrystalline microstructures containing twin grains with certain
morphologies, and apply it to generate representative volume elements. Second,
we develop a Fourier-based method with regularization for solving the effective
and local mechanical response of polycrystalline media using the
M\'eric-Cailletaud crystal plasticity constitutive law. Numerical results show
that, across configurations of twinning, the corresponding average effective
response is similar. Although differences were quantified, the effect of twins
on the yield stress is negligible in practice (less than $1\%$).
