The classical problem of the motion of a one-dimensional unsteady shock generated by a piston moving with velocity vp = ctn is extended to take into account thermal radiation effects by the similarity method of Taylor and Sedov. Gray gas and local thermodynamic equilibrium are assumed and a modification of the Schuster-Schwarzschild differential equation for the heat flux is adopted. The optical thickness is not restricted to be thin or thick, and the absorption coefficient is assumed to vary with the density and temperature. Numerical results indicate that the pressure and velocity are not affected much by the radiation, but the density, temperature and radiant heat flux are changed considerably.