  We investigate the impact of modified-gravity models on the Lyman-$\alpha$
power spectrum. Building a simple analytical modeling, based on a truncated
Zeldovich approximation, we estimate the intergalactic medium power spectrum
and the Lyman-$\alpha$ flux decrement power spectrum along the line of sight.
We recover the results of numerical simulations for $f(R)$-gravity models and
present new results for K-mouflage scenarios. We find that the shape of the
distortion due to the modified gravity depends on the model, through the
scale-dependence or not of their growth rate. This is more clearly seen in the
three-dimensional power spectrum than in the one-dimensional power spectrum,
where the line-of-sight integration smoothes the deviation. Whilst the
Lyman-$\alpha$ power spectrum does not provide competitive bounds for $f(R)$
theories, it could provide useful constraints for the K-mouflage models. Thus,
the efficiency of the Lyman-$\alpha$ power spectrum as a probe of
modified-gravity scenarios depends on the type of screening mechanism and the
related scale dependence it induces. The prospect of a full recovery of the
three-dimensional Lyman-$\alpha$ power spectrum from data would also lead to
stronger constraints and a better understanding of screening mechanisms.
