  Most recent extragalactic models of gamma-ray bursts consider the expansion
of a relativistic blast wave, emanating from a solar-mass type progenitor, into
the surrounding interstellar medium as the site for their activity. The popular
perception is that the optical afterglows result from the external shock
interface, while the prompt transient gamma-ray signal arises from multiple
shocks internal to the expansion. This paper illustrates a number of
acceleration properties of relativistic and ultrarelativistic shocks that
pertain to GRB models, by way of a standard Monte Carlo simulation.
Computations of the spectral shape, the range of spectral indices, and the
energy gain per shock crossing are presented, as functions of the shock speed
and the type of particle scattering.
