  We present theoretical expectations for non-thermal emission due to the bulk
Comptonization at the ultra-relativistic shock breakout. We calculate the
transfer of photons emitted from the shocked matter with a Monte Carlo code
fully taking into account special relativity. As a hydrodynamical model, we use
a self-similar solution of Nakayama & Shigeyama (2005). Our calculations reveal
that the spectral shape exhibits a double peak or a single peak depending on
the shock temperature at the shock breakout. If it is significantly smaller
than the rest energy of an electron, the spectrum has a double peak. We also
display a few example of light curves, and estimate the total radiation energy.
In comparison with observations of gamma-ray bursts, a part of the higher
energy component in the spectra and the total energy can be reproduced by some
parameter sets. Meanwhile, the lower energy counterpart in the Band function is
not reproduced by our results and the duration time seems too short to
represent the entire event of a gamma-ray burst. Therefore the subsequent phase
will constitute the lower energy part in the spectrum.
