The linear stability of shock waves in a radiating relativistic gas is
analyzed. According to the ratio between the sound speed and gas spee
d behind and ahead the front of discontinuity. the radiative shocks ar
e classified as slow and fast shock waves respectively. With the help
of the technique of dissipative energy integrals, it is proved that th
e fast shock waves are stable, An ill-posedness example for stability
problem for slow shocks is constructed.