  GRBs are nowadays a rather well understood phenomenon in the soft (KeV-MeV)
$\gamma$-ray energy band, while only a few GRBs have been observed at high
photon energies ($E_{\gamma} \ut > 1$ GeV). It is also widely recognized that
GRBs accelerate protons to relativistic energies and that dense media are often
present nearby the sources. Within this framework we compute in detail the
high-energy $\gamma$-ray flux from the decay of neutral pions produced through
the interaction of accelerate protons with nucleons in the surrounding medium.
We also take into account the local and intergalactic $\gamma$-ray absorption.
The presence of magnetic fields around the GRB sources causes the deflection of
the accelerated protons and so a temporal spread of the produced high-energy
$\gamma$-rays with respect to the signal in the soft $\gamma$-ray band.
Moreover, we analyze the possibility to detect the $\gamma$-ray signal in the
GeV-TeV energy range by the ARGO detector under construction in Tibet.
