We investigate the structure of the radiation field generated in high Mach number shock waves (supercritical shock waves [1]) which have a finite extension R in the direction perpendicular to the shock wave propagation. A simple analytical model allows us to calculate how the radiation field decreases with R for a medium with an homogeneous radiation emission in volume. We then perform a 3D radiative transfer calculation of the radiation field created by a stationary shock wave, and compare the predicted radiative energy density and flux with 1D calculations. We find that the variation of the radiation field with R follows the trend given by the analytical calculation. Finally, we perform radiative-hydrodynamical calculations to investigate further the variation of the radiation field with R and to estimate the decrease of the velocity of the radiative precursor withR.