  We calculate two-photon exchange amplitude for the elastic electron-pion
scattering in the dispersion-relation inspired approach, including both elastic
and inelastic contributions. The latter was modelled as a sum of \rho and
b_1(1235) meson contributions. We find that at Q^2 < 2 GeV^2 the elastic
contribution is dominant, similarly to electron-proton scattering case. At
higher Q^2 the inelastic contribution is not negligible, but still smaller than
the elastic one. We also explain observed rapid amplitude growth at backward
angles.
