Radiative shocks (also called supercritical shocks) are high Mach number shock waves that photoionize the medium ahead of the shock front and give rise to a radiative precursor. They are generated in the laboratory using high-energy or high-power lasers and are frequently present in a wide range of astronomical objects. Their modelization in one dimension has been the subject of numerous studies, but generalization to three dimensions is not straightforward. We calculate analytically the absorption of radiation in a gray uniform cylinder and show how it decreases with chiR, the product of the opacity chi and of the cylinder radius R. Simple formulas, whose validity range increases when chiR diminishes, are derived for the radiation field on the axis of symmetry. Numerical calculations in three dimensions of the radiative energy density, flux, and pressure created by a stationary shock wave show how the radiation decreases with R. Finally, the bidimensional structures of both the precursor and the radiation field are calculated with time-dependent radiation hydrodynamics numerical simulations and the influence of two-dimensional effects on the electron density, the temperature, the shock velocity, and the shock geometry are exhibited. These simulations show how the radiative precursor shortens, cools, and slows down when R is decreased.